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A281362
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a(0) = 1, a(1) = 2; for n>1, a(n) = a(n-1) + a(n-2) + floor(n/2).
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2
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1, 2, 4, 7, 13, 22, 38, 63, 105, 172, 282, 459, 747, 1212, 1966, 3185, 5159, 8352, 13520, 21881, 35411, 57302, 92724, 150037, 242773, 392822, 635608, 1028443, 1664065, 2692522, 4356602, 7049139, 11405757, 18454912, 29860686, 48315615, 78176319, 126491952
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 2*a(n-1) + a(n-2) - 3*a(n-3) + a(n-5) for n>4.
G.f.: (1 - x^2 + x^4) / ((1 - x)^2*(1 + x)*(1 - x - x^2)).
(End)
0 = 3 + a(n)*(-4 - 2*a(n) - a(n+1) + 6*a(n+2) - a(n+3)) + a(n+1)*(-1 + a(n+1) + a(n+2) - 2*a(n+3)) + a(n+2)*(+11 - 5*a(n+2) + 3*a(n+3)) + a(n+3)*(-6) for all n in Z. - Michael Somos, Jan 27 2017
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EXAMPLE
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G.f. = 1 + 2*x + 4*x^2 + 7*x^3 + 13*x^4 + 22*x^5 + 38*x^6 + 63*x^7 + ...
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MATHEMATICA
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CoefficientList[Series[(1-x^2+x^4)/((1-x)^2*(1+x)*(1-x-x^2)), {x, 0, 50}], x] (* G. C. Greubel, Jul 29 2018 *)
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PROG
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(PARI) Vec((1 - x^2 + x^4) / ((1 - x)^2*(1 + x)*(1 - x - x^2)) + O(x^50))
(PARI) {a(n) = my(m=n); if( n<0, m=-1-n); polcoeff( (1 - x^2 + x^4) / ((1 - x - x^2 + x^3) * (1 - (-1)^(n<0)*x - x^2)) + x * O(x^m), m)}; /* Michael Somos, Jan 27 2017 */
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 - x^2+x^4)/((1-x)^2*(1+x)*(1-x-x^2)))); // G. C. Greubel, Jul 29 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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