The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A098617

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A098617

G.f. A(x) satisfies: A(x*G(x)) = G(x), where G(x) is the g.f. for A098616(n) = Pell(n+1)*Catalan(n).
(history; published version)

#37 by Michel Marcus at Tue Apr 08 01:20:19 EDT 2014

STATUS

editing

proposed

Discussion

Tue Apr 15

23:01

Fung Lam: For A130783, there exists an alternative (correct but higher order) recurrence formula which is withheld for publication. In the present sequence, I have removed the second recurrence from my original submission. My interest in integer sequences arose from solving certain non-linear integral/differential equations; the solutions are expressed in terms of basic "elements" (a(0), a(1),...). If more than one recurrence formula exists for a sequence no matter how complicated it may appear, this fact implies that the solutions of the equations must be non-unique. In physics, the "solution patterns" can be built by selection from more than one set of the basic elements (satisfying all relevant physical principles).

Wed Apr 16

16:38

Vaclav Kotesovec: 1) Asymptotic formula is still wrong in the second term. I can't approve such formula.

16:44

Vaclav Kotesovec: 2) Regarding your recurrence, I agree with Peter.

#36 by Michel Marcus at Tue Apr 08 01:20:10 EDT 2014

FORMULA

Recurrence: (n+6)*a(n)=256*(n+1)*a(n-6)-128*(n+3)*a(n-4)+4*(5*n+23)*a(n-2), for even n. - _Fung Lam, _, Mar 31 2014

STATUS

proposed

editing

#35 by Fung Lam at Mon Apr 07 20:16:46 EDT 2014

STATUS

editing

proposed

#34 by Fung Lam at Mon Apr 07 20:16:32 EDT 2014

FORMULA

Recurrence: (n+6)*a(n)=256*(n+1)*a(n-6)-128*(n+3)*a(n-4)+4*(5*n+23)*a(n-2), for even n. - Fung Lam, Mar 31 2014

STATUS

proposed

editing

#33 by Michael Somos at Mon Apr 07 18:32:42 EDT 2014

STATUS

editing

proposed

#32 by Michael Somos at Mon Apr 07 18:32:22 EDT 2014

FORMULA

0 = a(n) * (+64*a(n+1) - 8*a(n+3)) + a(n+2) * (-8*a(n+1) + a(n+3)) if n>=0. - Michael Somos, Apr 07 2014

EXAMPLE

G.f. = 1 + 2*x + 6*x^2 + 16*x^3 + 46*x^4 + 128*x^5 + 364*x^6 + 1024*x^7 + ...

STATUS

proposed

editing

Discussion

Mon Apr 07

18:32

Michael Somos: Added more info.

#31 by N. J. A. Sloane at Fri Apr 04 14:54:40 EDT 2014

STATUS

editing

proposed

Discussion

Sat Apr 05

12:47

Vaclav Kotesovec: Please see discussion A130783, same theme.

Sun Apr 06

12:24

Peter Luschny: "My formulas may look complicated in algebra but they have meaningful interpretations." This might very well be the case but (almost) nobody who reads your formula without context can realize this special meaning you attach to them. Such things are better explained in a paper (or here on your wiki-page to which you can link). Without such an explanation the formulas look only strange, at least to me.

#30 by N. J. A. Sloane at Fri Apr 04 14:54:36 EDT 2014

STATUS

proposed

editing

#29 by Jon E. Schoenfield at Fri Apr 04 02:36:37 EDT 2014

STATUS

editing

proposed

Discussion

Fri Apr 04

14:54

N. J. A. Sloane: Dear Fung Lam, Could you perhaps resubmit your recurrence (or recurrences), but make it clear that it is only valid for even n?

#28 by Jon E. Schoenfield at Fri Apr 04 02:36:35 EDT 2014

COMMENTS

Hankel transform is 2^n. [_- _Paul Barry_ Jan 19 2011]

FORMULA

a(n) = sum{k=0..floor((n+1)/2), (C(n,k)-C(n,k-1))*A000129(n-2k+1)}. [_- _Paul Barry_ Jan 19 2011]

a(n) = 2^n*sum(j=0..n/2, binomial((n-1)/2,j)); [_. - _Vladimir Kruchinin_, May 18 2011]

STATUS

proposed

editing