A147833 Expansion of (4*x^2+x-1)/(12*x^3+4*x^2+x-1).

1, 0, 0, 12, 12, 60, 252, 636, 2364, 7932, 25020, 85116, 280380, 921084, 3063996, 10112892, 33421884, 110641404, 365683644, 1209311868, 3999743292, 13225194492, 43735910076, 144633607548, 478279581756, 1581644932860

Offset

0,4

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (1,4,12).

Formula

a(n) = a(n-1)+4*a(n-2)+12*a(n-3). G.f.: (4*x^2+x-1)/(12*x^3+4*x^2+x-1). [Colin Barker, Nov 02 2012]

Mathematica

Clear[M, v, f, g, x, n] M = {{0, 1, 0}, {0, 0, 1}, {12, 4, 1}} v[0] = {1, 0, 0} v[n_] := v[n] = M.v[n - 1] Table[v[n][[1]], {n, 0, 30}]
LinearRecurrence[{1, 4, 12}, {1, 0, 0}, 40] (* Harvey P. Dale, Jul 05 2019 *)

Crossrefs

Sequence in context: A298036 A119877 A307842 * A003877 A161196 A328531

Adjacent sequences: A147830 A147831 A147832 * A147834 A147835 A147836

Keyword

nonn,easy

Author

Roger L. Bagula and Gary W. Adamson, Nov 14 2008

Extensions

New name from Colin Barker and Joerg Arndt, Nov 02 2012

Status

approved