A367592 Expansion of 1/((1-x) * (1-4*x)^3).
1, 13, 109, 749, 4589, 26093, 140781, 730605, 3679725, 18097645, 87303661, 414459373, 1941186029, 8987616749, 41199871469, 187228759533, 844358755821, 3782116386285, 16838816966125, 74563177424365, 328550363440621, 1441256130749933, 6296699479008749
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (13,-60,112,-64).
Programs
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Mathematica
CoefficientList[Series[1/((1 - x)*(1 - 4*x)^3), {x, 0, 30}], x] (* Wesley Ivan Hurt, Aug 04 2025 *) -
PARI
a(n) = ((9*n^2+21*n+14)*4^(n+1)-2)/54;
Formula
G.f.: 1/((1-x) * (1-4*x)^3).
a(n) = ((9*n^2+21*n+14) * 4^(n+1) - 2)/54.
a(n) = 13*a(n-1) - 60*a(n-2) + 112*a(n-3) - 64*a(n-4). - Wesley Ivan Hurt, Aug 04 2025