The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A114361

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A114361

Let M(n) be the n X n matrix m(i,j)=min(i,j) for 1<=i,j<=n then a(n) is the trace of M(n)^(-9).
(history; published version)

#17 by Bruno Berselli at Tue Feb 23 05:26:11 EST 2021

STATUS

reviewed

approved

#16 by Joerg Arndt at Tue Feb 23 02:10:21 EST 2021

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proposed

reviewed

#15 by Michael De Vlieger at Mon Feb 22 17:54:43 EST 2021

STATUS

editing

proposed

#14 by Michael De Vlieger at Mon Feb 22 17:54:41 EST 2021

MATHEMATICA

Rest@ CoefficientList[Series[x (1 + 5776 x + 28614 x^2 + 13167 x^3 + 1053 x^4 + 9 x^5)/(1 - x)^2, {x, 0, 30}], x] (* Michael De Vlieger, Feb 22 2021 *)

STATUS

proposed

editing

#13 by Michel Marcus at Mon Feb 22 16:50:03 EST 2021

STATUS

editing

proposed

#12 by Michel Marcus at Mon Feb 22 16:49:33 EST 2021

FORMULA

a(n) = 48620n-106762, with n>4, a(1)=1, a(2)=5778, a(3)=40169, a(4)=87727.

From Colin Barker, Mar 18 2012: (Start)

a(n) = 2*a(n-1)-a(n-2) for n>6.

a(n) = 2*a(n-1)-a(n-2) for n>6. G.f.: x*(1+5776*x+28614*x^2+13167*x^3+1053*x^4+9*x^5)/(1-x)^2. [_Colin Barker_, Mar 18 2012](End)

STATUS

approved

editing

Discussion

Mon Feb 22

16:50

Michel Marcus: better layout like this

#11 by Alois P. Heinz at Mon Feb 22 15:45:32 EST 2021

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proposed

approved

#10 by Michel Marcus at Mon Feb 22 12:03:53 EST 2021

STATUS

editing

proposed

#9 by Michel Marcus at Mon Feb 22 12:03:48 EST 2021

COMMENTS

More generally for any n>=floor((m+1)/2) the trace of M(n)^(-m) = binomial(2*m,m)*n-2^(2*m-1)+binomial(2*m-1,m).

LINKS

<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

FORMULA

a(n) = 2*a(n-1)-a(n-2) for n>6. G.f.: x*(1+5776*x+28614*x^2+13167*x^3+1053*x^4+9*x^5)/(1-x)^2. [_Colin Barker, _, Mar 18 2012]

CROSSREFS

Cf. A114358, A114359, A114360.

STATUS

approved

editing

#8 by Russ Cox at Fri Mar 30 18:39:24 EDT 2012

AUTHOR

_Benoit Cloitre (benoit7848c(AT)orange.fr), _, Feb 09 2006

Discussion

Fri Mar 30

18:39

OEIS Server: https://oeis.org/edit/global/216