A129997 - OEIS

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A129997

a(n) = 4*a(n-1) + (n-6)*a(n-2).

0, 1, 4, 14, 52, 208, 884, 3952, 18460, 89648, 450892, 2341456, 12522068, 68819920, 387978292, 2240112368, 13228210684, 79794191152, 491143503500, 3081692690128, 19693923313012, 128082776294096, 847127801497588

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..23.

FORMULA

a(n) = 4*a(n-1) + (n-6)*a(n-2). - Vaclav Kotesovec, Oct 20 2012

a(n) ~ 26*sqrt(2)*exp(4*sqrt(n)-n/2-4)*n^(n/2-5/2)*(1-19/(3*sqrt(n))+1/(6*n)) . - Vaclav Kotesovec, Oct 20 2012

MATHEMATICA

M[n_] := {{0, 1}, {-4 + n, 4}} v[0] = {0, 1}; v[n_] := v[n] = M[n].v[m - 1] a = Table[v[m][[1]], {m, 0, 30}]

RecurrenceTable[{a[n] == 4*a[n-1] + (n-6)*a[n-2], a[1]==0, a[2]==1}, a, {n, 20}] (* Vaclav Kotesovec, Oct 20 2012 *)

PROG

(Magma) [n le 2 select n-1 else 4*Self(n-1)+(n-6)*Self(n-2): n in [1..30]]; // Vincenzo Librandi, May 24 2013

CROSSREFS

Sequence in context: A345242 A370891 A284765 * A308023 A149489 A125783

Adjacent sequences: A129994 A129995 A129996 * A129998 A129999 A130000

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Jun 15 2007

EXTENSIONS

New name from Vaclav Kotesovec, Oct 20 2012

STATUS

approved