A094623 Expansion of g.f. x*(1+10*x)/((1-x)*(1-10*x^2)).

0, 1, 11, 21, 121, 221, 1221, 2221, 12221, 22221, 122221, 222221, 1222221, 2222221, 12222221, 22222221, 122222221, 222222221, 1222222221, 2222222221, 12222222221, 22222222221, 122222222221, 222222222221, 1222222222221

Offset: 0

Author

Paul Barry, May 15 2004

Keywords

• easy
• nonn
• base

Comments

Previous name was: Sequence whose n-th term digits sum to n.

n-th term digits are reversals of A094624(n).

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,10,-10).

Crossrefs

Cf. A094624, A094625, A094626.

Programs

Mathematica

LinearRecurrence[{1, 10, -10}, {0, 1, 11}, 30] (* Paolo Xausa, Feb 22 2024 *)

Formula

G.f.: x*(1+10*x)/((1-x)*(1-10*x^2)).

a(n) = (10^(n/2)/2)*(11/9 + 2*sqrt(10)/9 - (2*sqrt(10)/9 - 11/9)*(-1)^n) - 11/9.

E.g.f.: (11*(cosh(sqrt(10)*x) - cosh(x)) + 2*sqrt(10)*sinh(sqrt(10)*x) - 11*sinh(x))/9. - Stefano Spezia, Feb 21 2024