A121957 Expansion of x^2*(43 -11*x -148*x^2 +23*x^3)/(1 -2*x -7*x^2 +7*x^3 +12*x^4 -2*x^5).

0, 43, 75, 303, 853, 2786, 8608, 27261, 85646, 270137, 851245, 2684011, 8462548, 26684106, 84143305, 265331874, 836695587, 2638426981, 8320048505, 26236520890, 82734709152, 260896992401, 822717574538, 2594372978149

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,7,-7,-12,2).

Formula

From R. J. Mathar, Apr 04 2009: (Start)

a(n) = 2*a(n-1) + 7*a(n-2) - 7*a(n-3) - 12*a(n-4) + 2*a(n-5).

G.f.: x^2*(43 -11*x -148*x^2 +23*x^3)/(1 -2*x -7*x^2 +7*x^3 +12*x^4 -2*x^5). (End)

Mathematica

M = {{0, 1, 0, 0, 1, 1, 0, 0, 0, 1}, {1, 0, 1, 0, 0, 1, 1, 0, 0, 0}, {0, 1, 0, 1, 0, 0, 1, 1, 0, 0}, {0, 0, 1, 0, 1, 0, 0, 0, 1, 0}, {1, 0, 0, 1, 0, 0, 0, 0, 1, 1}, {1, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 1, 0, 0, 0, 0, 0}};
v[1]= Table[Fibonacci[n], {n, 0, 9}]; v[n_]:= v[n]= M.v[n-1];
Table[Floor[v[n][[1]]], {n, 1, 50}]

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 50); [0] cat Coefficients(R!( x^2*(43 -11*x -148*x^2 +23*x^3)/(1 -2*x -7*x^2 +7*x^3 +12*x^4 -2*x^5) )); // G. C. Greubel, Jul 12 2021
(Sage)
def A121957_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( x^2*(43-11*x-148*x^2+23*x^3)/(1-2*x-7*x^2+7*x^3+12*x^4 -2*x^5) ).list()
a=A121957_list(50); a[1:]  # G. C. Greubel, Jul 12 2021

Crossrefs

Sequence in context: A176925 A080177 A238248 * A118075 A236839 A183074

Adjacent sequences: A121954 A121955 A121956 * A121958 A121959 A121960

Keyword

nonn,easy

Author

Roger L. Bagula, Sep 01 2006

Extensions

Edited by G. C. Greubel, Jul 12 2021

Status

approved