A014907 a(1)=1, a(n) = 22*a(n-1) + n.

1, 24, 531, 11686, 257097, 5656140, 124435087, 2737571922, 60226582293, 1324984810456, 29149665830043, 641292648260958, 14108438261741089, 310385641758303972, 6828484118682687399, 150226650611019122794, 3304986313442420701485, 72709698895733255432688, 1599613375706131619519155

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 (24,-45,22).

Crossrefs

Row n=22 of A126885.

Programs

Magma

I:=[1, 24, 531]; [n le 3 select I[n] else 24*Self(n-1) - 45*Self(n-2) + 22*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 19 2012

Mathematica

LinearRecurrence[{24, -45, 22}, {1, 24, 531}, 20] (* Vincenzo Librandi, Oct 19 2012 *)

Maxima

a[1]:1$
a[2]:24$
a[3]:531$
a[n]:=24*a[n-1]-45*a[n-2]+22*a[n-3]$
A014907(n):=a[n]$
makelist(A014907(n),n,1,30); /* Martin Ettl, Nov 06 2012 */

Formula

a(1)=1, a(2)=24, a(3)=531, a(n) = 24*a(n-1) - 45*a(n-2) + 22*a(n-3). - Vincenzo Librandi, Oct 19 2012

From Elmo R. Oliveira, Mar 29 2025: (Start)

G.f.: x/((1-22*x)*(x-1)^2).

E.g.f.: exp(x)*(22*exp(21*x) - 21*x - 22)/441.

a(n) = (22^(n+1) - 21*n - 22)/441. (End)