A368530 a(n) = Sum_{k=1..n} k^3 * 4^(n-k).

0, 1, 12, 75, 364, 1581, 6540, 26503, 106524, 426825, 1708300, 6834531, 27339852, 109361605, 437449164, 1749800031, 6999204220, 27996821793, 111987293004, 447949178875, 1791796723500, 7167186903261, 28668747623692, 114674990506935, 458699962041564

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (8,-22,28,-17,4).

Formula

G.f.: x * (1+4*x+x^2)/((1-4*x) * (1-x)^4).

a(n) = 8*a(n-1) - 22*a(n-2) + 28*a(n-3) - 17*a(n-4) + 4*a(n-5).

a(n) = (11*4^(n+1) - (9*n^3 + 36*n^2 + 60*n + 44))/27.

a(0) = 0; a(n) = 4*a(n-1) + n^3.

Prog

(PARI) a(n) = sum(k=1, n, k^3*4^(n-k));

Crossrefs

Cf. A000578, A000537, A213575, A066999.

Cf. A097788, A368525.

Cf. A014825, A368529.

Sequence in context: A092867 A292532 A053310 * A006235 A009642 A051104

Adjacent sequences: A368527 A368528 A368529 * A368531 A368532 A368533

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 29 2023

Status

approved