A014899 a(n) = (16^(n+1) - 15*n - 16)/225.

0, 1, 18, 291, 4660, 74565, 1193046, 19088743, 305419896, 4886718345, 78187493530, 1250999896491, 20015998343868, 320255973501901, 5124095576030430, 81985529216486895, 1311768467463790336, 20988295479420645393, 335812727670730326306, 5373003642731685220915

Offset: 0

Author

N. J. A. Sloane, Olivier Gérard

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (18,-33,16).

Crossrefs

Row n=16 of A126885.

Programs

Magma

I:=[0, 1, 18]; [n le 3 select I[n] else 18*Self(n-1) - 33*Self(n-2) + 16*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 20 2012

Maple

a:=n->sum((16^(n-j)-1)/15,j=0..n): seq(a(n), n=1..16); # Zerinvary Lajos, Jan 05 2007
n0:=20: tabl:=array(1..n0-1): for n from 0 to n0 do: tabl[n+1]:=(4^(2*n+2) - 15*n - 16)/225:od:print( tabl): # Michel Lagneau, Apr 26 2010

Mathematica

s=0;lst={};Do[AppendTo[lst,s+=s+=s+=s+=s+=n],{n,5!}];lst/16 (* Vladimir Joseph Stephan Orlovsky, Oct 20 2009 *)
Table[(16^(n+1)-15*n-16)/225,{n,0,20}] (* Harvey P. Dale, Dec 20 2010 *)
LinearRecurrence[{18, -33, 16}, {0, 1, 18}, 20] (* Vincenzo Librandi, Oct 20 2012 *)

Maxima

A014899(n):=(16^(n+1)-15*n-16)/225$ makelist(A014899(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

a(n)=(16^(n+1)-15*n)\225 \\ Charles R Greathouse IV, May 15 2013

Formula

a(n) = 16*a(n-1) + n = 18*a(n-1) - 33*a(n-2) + 16*a(n-3).

G.f.: x/((1-16*x)*(x-1)^2). - R. J. Mathar, Apr 29 2010

E.g.f.: exp(x)*(16*exp(15*x) - 15*x - 16)/225. - Elmo R. Oliveira, Mar 31 2025

Extensions

a(0) added by R. J. Mathar, Apr 29 2010