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

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (18,-33,16).

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

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 *)

Prog

(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
(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

Crossrefs

Sequence in context: A226998 A098303 A232154 * A048447 A167713 A219670

Adjacent sequences: A014896 A014897 A014898 * A014900 A014901 A014902

Keyword

nonn,easy

Author

N. J. A. Sloane, Olivier Gérard

Extensions

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

Status

approved