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A014896
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a(1) = 1, a(n) = 13*a(n-1) + n.
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3
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1, 15, 198, 2578, 33519, 435753, 5664796, 73642356, 957350637, 12445558291, 161792257794, 2103299351334, 27342891567355, 355457590375629, 4620948674883192, 60072332773481512, 780940326055259673, 10152224238718375767, 131978915103338884990
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = 15*a(n-1)-27*a(n-2)+13*a(n-3), with a(1)=1, a(2)=15, a(3)=198. - Vincenzo Librandi, Oct 20 2012
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MAPLE
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a:=n->sum((13^(n-j)-1)/12, j=0..n): seq(a(n), n=1..17); # Zerinvary Lajos, Jan 05 2007
a:= n-> (Matrix([[1, 0, 1], [1, 1, 1], [0, 0, 13]])^n)[2, 3]:
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MATHEMATICA
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LinearRecurrence[{15, -27, 13}, {1, 15, 198}, 20] (* Vincenzo Librandi, Oct 20 2012 *)
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PROG
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(Magma) I:=[1, 15, 198]; [n le 3 select I[n] else 15*Self(n-1) - 27*Self(n-2)+ 13*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 20 2012
(Maxima)
a[1]:1$
a[2]:15$
a[3]:198$
a[n]:=15*a[n-1]-27*a[n-2]+13*a[n-3]$
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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