A353097 a(1) = 5; for n > 1, a(n) = 6*a(n-1) + 6 - n.

5, 34, 207, 1244, 7465, 44790, 268739, 1612432, 9674589, 58047530, 348285175, 2089711044, 12538266257, 75229597534, 451377585195, 2708265511160, 16249593066949, 97497558401682, 584985350410079, 3509912102460460, 21059472614762745, 126356835688576454

Offset: 1

Author

Seiichi Manyama, Apr 23 2022

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (8,-13,6).

Crossrefs

Cf. A064617, A353094, A353095, A353096, A353098, A353099, A353100.

Cf. A014829.

Programs

Mathematica

LinearRecurrence[{8, -13, 6}, {5, 34, 207}, 22] (* Amiram Eldar, Apr 23 2022 *)

PARI

my(N=30, x='x+O('x^N)); Vec(x*(5-6*x)/((1-x)^2*(1-6*x)))

PARI

a(n) = (4*6^(n+1)+5*n-24)/25;

PARI

b(n, k) = sum(j=0, n-1, (k-n+j)*k^j);
a(n) = b(n, 6);

Formula

G.f.: x * (5 - 6*x)/((1 - x)^2 * (1 - 6*x)).

a(n) = 8*a(n-1) - 13*a(n-2) + 6*a(n-3).

a(n) = 4*A014829(n) + n.

a(n) = (4*6^(n+1) + 5*n - 24)/25.

a(n) = Sum_{k=0..n-1} (6 - n + k) * 6^k.

E.g.f.: exp(x)*(24*exp(5*x) + 5*x - 24)/25. - Stefano Spezia, May 28 2023