A014941 a(1)=1, a(n) = n*23^(n-1) + a(n-1).

1, 47, 1634, 50302, 1449507, 40067565, 1076318788, 28314922364, 733113789893, 18744640404523, 474436263754662, 11908153358721786, 296798270974985959, 7353307338085529321, 181245852206166776456, 4447409619636426706168, 108701786686213403738505, 2647602498778146844408359

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 1..500
• Index entries for linear recurrences with constant coefficients, signature (47,-575,529).

Programs

Mathematica

A014941[n_] := (23^n*(22*n - 1) + 1)/484; Array[A014941, 25] (* or *)
LinearRecurrence[{47, -575, 529}, {1, 47, 1634}, 25] (* Paolo Xausa, May 29 2025 *)

PARI

a(n) = (1+23^n*(22*n-1))/484; \\ Jinyuan Wang, Mar 11 2020

PARI

my(x='x+O('x^19)); Vec(-x/((x-1)*(23*x-1)^2)) \\ Elmo R. Oliveira, May 22 2025

Formula

G.f.: x/((1 - x)*(1 - 23*x)^2). - Stefano Spezia, Mar 11 2020

From Elmo R. Oliveira, May 22 2025: (Start)

E.g.f.: exp(x)*(1 + exp(22*x)*(506*x - 1))/484.

a(n) = (23^n*(22*n - 1) + 1)/484.

a(n) = 46*a(n-1) - 529*a(n-2) + 1 for n > 2.

a(n) = 47*a(n-1) - 575*a(n-2) + 529*a(n-3) for n >= 4. (End)

Extensions

More terms from Elmo R. Oliveira, May 22 2025