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A022410
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a(n) = a(n-1) + a(n-2) + 1 for n>1, a(0)=3, a(1)=11.
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1
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3, 11, 15, 27, 43, 71, 115, 187, 303, 491, 795, 1287, 2083, 3371, 5455, 8827, 14283, 23111, 37395, 60507, 97903, 158411, 256315, 414727, 671043, 1085771, 1756815, 2842587, 4599403, 7441991, 12041395, 19483387, 31524783, 51008171, 82532955, 133541127
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: (3 + 5*x - 7*x^2) / ((x - 1)*(x^2 + x - 1)).
(End)
a(n) = 2^(-n)*(-2^n + 2*(1-sqrt(5))^(1+n) + 2*(1+sqrt(5))^(1+n)).
a(n) = 2*a(n-1) - a(n-3) for n>2.
(End)
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MATHEMATICA
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LinearRecurrence[{2, 0, -1}, {3, 11, 15}, 40] (* Bruno Berselli, Jul 27 2017 *)
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PROG
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(Python)
from sympy import lucas
def a(n): return 4 * lucas(n + 1) - 1
(PARI) Vec((3+5*x-7*x^2)/((x-1)*(x^2+x-1)) + O(x^50)) \\ Colin Barker, Jul 27 2017
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((3+5*x-7*x^2)/((x-1)*(x^2+x-1)))); // G. C. Greubel, Feb 28 2018
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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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