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A014882
a(1) = 1, a(n) = 12*a(n-1) + n.
2
1, 14, 171, 2056, 24677, 296130, 3553567, 42642812, 511713753, 6140565046, 73686780563, 884241366768, 10610896401229, 127330756814762, 1527969081777159, 18335628981325924, 220027547775911105, 2640330573310933278, 31683966879731199355
OFFSET
1,2
FORMULA
a(n) = 14*a(n-1)-25*a(n-2)+12*a(n-3), with a(1)=1, a(2)=14, a(3)=171. - Vincenzo Librandi, Oct 20 2012
G.f.: x/((1-12*x)*(1-x)^2). - Jinyuan Wang, Mar 11 2020
MAPLE
a:=n->sum((12^(n-j)-1^(n-j))/11, j=0..n): seq(a(n), n=1..17); # Zerinvary Lajos, Jan 12 2007
a:= n-> (Matrix([[1, 0, 1], [1, 1, 1], [0, 0, 12]])^n)[2, 3]:
seq(a(n), n=1..17); # Alois P. Heinz, Aug 06 2008
MATHEMATICA
LinearRecurrence[{14, -25, 12}, {1, 14, 171}, 201] (* Vincenzo Librandi, Oct 20 2012 *)
PROG
(Magma) I:=[1, 14, 171]; [n le 3 select I[n] else 14*Self(n-1) - 25*Self(n-2)+ 12*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 20 2012
CROSSREFS
Sequence in context: A341500 A254811 A099158 * A048443 A191690 A016136
KEYWORD
nonn
STATUS
approved