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A014881
a(1)=1, a(n) = 11*a(n-1)+n.
3
1, 13, 146, 1610, 17715, 194871, 2143588, 23579476, 259374245, 2853116705, 31384283766, 345227121438, 3797498335831, 41772481694155, 459497298635720, 5054470284992936, 55599173134922313, 611590904484145461, 6727499949325600090
OFFSET
1,2
FORMULA
a(n) = 13*a(n-1)-23*a(n-2)+11*a(n-3), with a(1)=1, a(2)=13, a(3)=146. - Vincenzo Librandi, Oct 20 2012
G.f.: x/((1-11*x)*(1-x)^2). - Jinyuan Wang, Mar 11 2020
MAPLE
a:= n-> (Matrix([[1, 0, 1], [1, 1, 1], [0, 0, 11]])^n)[2, 3]:
seq(a(n), n=1..17); # Alois P. Heinz, Aug 06 2008
MATHEMATICA
LinearRecurrence[{13, -23, 11}, {1, 13, 146}, 20] (* Vincenzo Librandi, Oct 20 2012 *)
PROG
(Magma) I:=[1, 13, 146]; [n le 3 select I[n] else 13*Self(n-1) - 23*Self(n-2)+ 11*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 20 2012
CROSSREFS
Sequence in context: A297223 A199023 A152585 * A048442 A353107 A051524
KEYWORD
nonn
STATUS
approved