A014901 a(1)=1, a(n) = 18*a(n-1) + n.

1, 20, 363, 6538, 117689, 2118408, 38131351, 686364326, 12354557877, 222382041796, 4002876752339, 72051781542114, 1296932067758065, 23344777219645184, 420205989953613327, 7563707819165039902, 136146740744970718253, 2450641333409472928572, 44111544001370512714315

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (20,-37,18).

Formula

a(1)=1, a(2)=20, a(3)=363, a(n) = 20*a(n-1) - 37*a(n-2) + 18*a(n-3). - Vincenzo Librandi, Oct 20 2012

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

G.f.: x/((1-18*x)*(1-x)^2).

E.g.f.: exp(x)*(18*exp(17*x) - 17*x - 18)/289.

a(n) = (18^(n+1) - 17*n - 18)/289. (End)

a(-1-n) = A014935(n)/18^n for all n in Z. - Michael Somos, Mar 29 2025

Mathematica

LinearRecurrence[{20, -37, 18}, {1, 20, 363}, 20] (* Vincenzo Librandi, Oct 20 2012 *)
nxt[{n_, a_}]:={n+1, 18a+n+1}; NestList[nxt, {1, 1}, 20][[All, 2]] (* Harvey P. Dale, Oct 08 2017 *)

Prog

(Magma) I:=[1, 20, 363]; [n le 3 select I[n] else 20*Self(n-1) - 37*Self(n-2) + 18*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 20 2012
(Maxima)
a[1]:1$
a[2]:20$
a[3]:363$
a[n]:=20*a[n-1]-37*a[n-2]+18*a[n-3]$
A014901(n):=a[n]$
makelist(A014901(n), n, 1, 30); /* Martin Ettl, Nov 06 2012 */

Crossrefs

Row n=18 of A126885.

Cf. A014935.

Sequence in context: A115100 A049683 A228330 * A290581 A000564 A365415

Adjacent sequences: A014898 A014899 A014900 * A014902 A014903 A014904

Keyword

nonn,easy

Author

N. J. A. Sloane, Olivier Gérard

Status

approved