A158778 G.f.: (1+3*x+12*x^2+48*x^3)/(1-x-256*x^4).

1, 4, 16, 64, 320, 1344, 5440, 21824, 103744, 447808, 1840448, 7427392, 33985856, 148624704, 619779392, 2521191744, 11221570880, 49269495104, 207933019456, 853358105920, 3726080251200, 16339070997824, 69569923978560

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,256).

Formula

a(n)= +a(n-1) + 256*a(n-4).

Mathematica

Clear[M, v, t, n];
M = {{0, t, 0, 0}, {0, 0, t, 0}, {0, 0, 0, t}, {t, 0, 0, 1/t}};
v[0] = {1, 1, 1, 1};
v[n_] := v[n] = M.v[n - 1];
CharacteristicPolynomial[M, x];
t = 2;
a = Table[t^n*v[n][[1]], {n, 0, 30}]
LinearRecurrence[{1, 0, 0, 256}, {1, 4, 16, 64}, 30] (* Harvey P. Dale, Nov 27 2024 *)

Prog

(PARI) Vec((1+3*x+12*x^2+48*x^3)/(1-x-256*x^4)+O(x^44))

Crossrefs

Sequence in context: A212443 A294036 A097679 * A227313 A381551 A155518

Adjacent sequences: A158775 A158776 A158777 * A158779 A158780 A158781

Keyword

nonn,easy

Author

Roger L. Bagula, Mar 26 2009

Status

approved