A014909 a(1)=1, a(n) = 23*a(n-1) + n.

1, 25, 578, 13298, 305859, 7034763, 161799556, 3721389796, 85591965317, 1968615202301, 45278149652934, 1041397442017494, 23952141166402375, 550899246827254639, 12670682677026856712, 291425701571617704392, 6702791136147207201033, 154164196131385765623777, 3545776511021872609346890

Offset: 1

Author

N. J. A. Sloane, Olivier Gérard

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (25,-47,23).

Crossrefs

Row n=23 of A126885.

Programs

Magma

I:=[1, 25, 578]; [n le 3 select I[n] else 25*Self(n-1)-47*Self(n-2)+23*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Feb 05 2012

Mathematica

Transpose[NestList[{First[#]+1,23Last[#]+First[#]+1}&,{1,1},20]][[2]] (* or *) LinearRecurrence[{25,-47,23},{1,25,578},20] (* Harvey P. Dale, Feb 05 2012 *)

Formula

From Harvey P. Dale, Feb 05 2012: (Start)

a(1)=1, a(2)=25, a(3)=578, a(n) = 25*a(n-1) - 47*a(n-2) + 23*a(n-3).

G.f.: -x/((-1+x)^2*(-1+23*x)). (End)

From Elmo R. Oliveira, Mar 30 2025: (Start)

E.g.f.: exp(x)*(23*exp(22*x) - 22*x - 23)/484.

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