A094625 Expansion of g.f. x*(2+22*x+11*x^2)/((x-1)*(1+x)*(10*x^2-1)).

0, 2, 22, 33, 242, 343, 2442, 3443, 24442, 34443, 244442, 344443, 2444442, 3444443, 24444442, 34444443, 244444442, 344444443, 2444444442, 3444444443, 24444444442, 34444444443, 244444444442, 344444444443, 2444444444442

Offset: 0

Author

Paul Barry, May 15 2004

Keywords

• easy
• nonn
• base

Comments

Previous name: Palindromic sequence whose n-th term digits sum to 2n.

Links

• Paolo Xausa, 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, A094624.

Programs

Mathematica

LinearRecurrence[{0, 11, 0, -10}, {0, 2, 22, 33}, 30] (* Paolo Xausa, Feb 22 2024 *)

Formula

a(n) = 10^(n/2)*(31*sqrt(10)/180 + 11/9 - (31*sqrt(10)/180 - 11/9)*(-1)^n) - (-1)^n/2 - 35/18;

a(n) = A094623(n) + A094624(n).

G.f.: x*(2+22*x+11*x^2) / ( (x-1)*(1+x)*(10*x^2-1) ). - R. J. Mathar, Nov 27 2014

E.g.f.: (220*(cosh(sqrt(10)*x) - cosh(x)) + 31*sqrt(10)*sinh(sqrt(10)*x) - 130*sinh(x))/90. - Stefano Spezia, Feb 21 2024