A094624 Expansion of g.f. x*(1+11*x+x^2)/((1-x)*(1+x)*(1-10*x^2)).

0, 1, 11, 12, 121, 122, 1221, 1222, 12221, 12222, 122221, 122222, 1222221, 1222222, 12222221, 12222222, 122222221, 122222222, 1222222221, 1222222222, 12222222221, 12222222222, 122222222221, 122222222222, 1222222222221, 1222222222222, 12222222222221

Offset: 0

Author

Paul Barry, May 15 2004

Keywords

• nonn
• base
• easy

Comments

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

n-th term digits are reversals of A094623(n).

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,11,0,-10).

Crossrefs

Cf. A094623, A094625, A094626.

Programs

Mathematica

LinearRecurrence[{0, 11, 0, -10}, {0, 1, 11, 12}, 30] (* Paolo Xausa, Feb 22 2024 *)

PARI

concat(0, Vec(x*(1+11*x+x^2)/((1-x)*(1+x)*(1-10*x^2)) + O(x^40))) \\ Colin Barker, Dec 01 2015

Formula

a(n) = 10^(n/2)*(11/18 + 11*sqrt(10)/180 - (11*sqrt(10)/180 - 11/18)(-1)^n) - 13/18 - (-1)^n/2.

From Colin Barker, Dec 01 2015: (Start)

a(n) = 11*a(n-2) - 10*a(n-4) for n > 3.

G.f.: x*(1+11*x+x^2) / ((1-x)*(1+x)*(1-10*x^2)). (End)

E.g.f.: (110*(cosh(sqrt(10)*x) - cosh(x)) + 11*sqrt(10)*sinh(sqrt(10)*x) - 20*sinh(x))/90. - Stefano Spezia, Feb 21 2024