A353095 a(1) = 3; for n > 1, a(n) = 4*a(n-1) + 4 - n.

3, 14, 57, 228, 911, 3642, 14565, 58256, 233019, 932070, 3728273, 14913084, 59652327, 238609298, 954437181, 3817748712, 15270994835, 61083979326, 244335917289, 977343669140, 3909374676543, 15637498706154, 62549994824597, 250199979298368, 1000799917193451

Offset: 1

Author

Seiichi Manyama, Apr 23 2022

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-9,4).

Crossrefs

Cf. A064617, A353094, A353096, A353097, A353098, A353099, A353100.

Cf. A014825.

Programs

Mathematica

LinearRecurrence[{6, -9, 4}, {3, 14, 57}, 25] (* Amiram Eldar, Apr 23 2022 *)

PARI

my(N=30, x='x+O('x^N)); Vec(x*(3-4*x)/((1-x)^2*(1-4*x)))

PARI

a(n) = (2*4^(n+1)+3*n-8)/9;

PARI

b(n, k) = sum(j=0, n-1, (k-n+j)*k^j);
a(n) = b(n, 4);

Formula

G.f.: x * (3 - 4*x)/((1 - x)^2 * (1 - 4*x)).

a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3).

a(n) = 2 * A014825(n) + n.

a(n) = (2*4^(n+1) + 3*n - 8)/9.

a(n) = Sum_{k=0..n-1} (4 - n + k) * 4^k.

E.g.f.: exp(x)*(8*exp(3*x) + 3*x - 8)/9. - Stefano Spezia, May 28 2023