A353099 a(1) = 7; for n>1, a(n) = 8 * a(n-1) + 8 - n.

7, 62, 501, 4012, 32099, 256794, 2054353, 16434824, 131478591, 1051828726, 8414629805, 67317038436, 538536307483, 4308290459858, 34466323678857, 275730589430848, 2205844715446775, 17646757723574190, 141174061788593509, 1129392494308748060

Offset: 1

Author

Seiichi Manyama, Apr 23 2022

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-17,8).

Crossrefs

Cf. A064617, A353094, A353095, A353096, A353097, A353098, A353100.

Cf. A014831.

Programs

Mathematica

LinearRecurrence[{10, -17, 8}, {7, 62, 501}, 20] (* Amiram Eldar, Apr 23 2022 *)

PARI

my(N=30, x='x+O('x^N)); Vec(x*(7-8*x)/((1-x)^2*(1-8*x)))

PARI

a(n) = (6*8^(n+1)+7*n-48)/49;

PARI

b(n, k) = sum(j=0, n-1, (k-n+j)*k^j);
a(n) = b(n, 8);

Formula

G.f.: x * (7 - 8 * x)/((1 - x)^2 * (1 - 8 * x)).

a(n) = 10*a(n-1) - 17*a(n-2) + 8*a(n-3).

a(n) = 6 * A014831(n) + n.

a(n) = (6*8^(n+1) + 7*n - 48)/49.

a(n) = Sum_{k=0..n-1} (8 - n + k)*8^k.

E.g.f.: exp(x)*(48*(exp(7*x) - 1) + 7*x)/49. - Stefano Spezia, May 29 2023