The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A296000

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A296000

Solution of the complementary equation a(n) = a(0)*b(n-1) + a(1)*b(n-2) + ... + a(n-1)*b(0), where a(0) = 1, a(1) = 3, b(0) = 2, and (a(n)) and (b(n)) are increasing complementary sequences.
(history; published version)

#18 by Alois P. Heinz at Wed Sep 23 10:51:02 EDT 2020

STATUS

editing

approved

#17 by Alois P. Heinz at Wed Sep 23 10:50:02 EDT 2020

EXTENSIONS

Conjectured Incorrect conjectured g.f. removed by Georg Fischer, Sep 23 2020

STATUS

proposed

editing

#16 by Georg Fischer at Wed Sep 23 09:16:28 EDT 2020

STATUS

editing

proposed

Discussion

Wed Sep 23

09:23

Andrew Howroyd: Do you have  a way to calculate these - it would be nice to add a b-file (so that anyone looking for linear recs can rule it out as a possibility pragmatically). If not, the extension probably does the trick.

#15 by Georg Fischer at Wed Sep 23 09:13:52 EDT 2020

FORMULA

Conjectures from Colin Barker, Dec 08 2017: (Start)

G.f.: (1 - x)^2*(1 + x) / (1 - 4*x + x^2 + x^3 - x^8 + x^9).

a(n) = 4*a(n-1) - a(n-2) - a(n-3) + a(n-8) - a(n-9) for n > 8.

(End)

EXTENSIONS

Conjectured g.f. removed by Georg Fischer, Sep 23 2020

STATUS

approved

editing

Discussion

Wed Sep 23

09:16

Georg Fischer: a(36, 37)=10079273721355653765, 36801327034309204815, conjectured g.f. = 10079273721355653764, 36801327034309204809

#14 by N. J. A. Sloane at Sun Jan 07 23:26:05 EST 2018

STATUS

proposed

approved

#13 by Clark Kimberling at Sat Jan 06 09:17:18 EST 2018

STATUS

editing

proposed

#12 by Clark Kimberling at Sat Jan 06 09:02:24 EST 2018

MATHEMATICA

$RecursionLimit = Infinity;

Table[a[n], {n, 0, 100}]; (* A296000 *)

STATUS

approved

editing

#11 by Michel Marcus at Mon Dec 11 10:42:00 EST 2017

STATUS

reviewed

approved

#10 by Joerg Arndt at Mon Dec 11 10:41:42 EST 2017

STATUS

proposed

reviewed

#9 by Jon E. Schoenfield at Sat Dec 09 12:29:35 EST 2017

STATUS

editing

proposed