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(PARI) Vec(x*(x-2)*(x^2-x+1) / ((x^2+x-1)*(x-1)^2) + O(x^50)) \\ Colin Barker, Mar 12 2017

Nonhomogeneous three-term sequence a(n) = a(n-1)+) + a(n-2)+) + n.

2, 3, 8, 15, 28, 49, 84, 141, 234, 385, 630, 1027, 1670, 2711, 4396, 7123, 11536, 18677, 30232, 48929, 79182, 128133, 207338, 335495, 542858, 878379, 1421264, 2299671, 3720964, 6020665, 9741660, 15762357, 25504050, 41266441, 66770526, 108037003, 174807566

Colin Barker, <a href="/A179991/b179991.txt">Table of n, a(n) for n = 1..1000</a>

G.Ff.: x*(x-2)*(x^2-x+1) / ( (x^2+x-1)*(x-1)^2 ).

From Colin Barker, Mar 12 2017: (Start)

a(n) = 2^(-n)*(-3*2^n+(1-sqrt(5))^(1+n) + (1+sqrt(5))^n + sqrt(5)*(1+sqrt(5))^n - 2^n*n).

a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) for n>4.

(End)

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<a href="/index/Rec#order_04">Index to sequencesentries withfor linear recurrences with constant coefficients</a>, signature (3,-2,-1,1).

OEIS Server: https://oeis.org/edit/global/2439

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Cf. A000045., A022319 (first differences).

nonn,easy,changed

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<a href="/index/Rec#order_04">Index to sequences with linear recurrences with constant coefficients</a>, signature (3,-2,-1,1).

G.F.: x*(x^3-3*x^2+3*x-2)/()*(x^42-x^3-2*+1) / ( (x^2+3*x-1)*(x-1).)^2 ).

G.f. multiplied by x. - R. J. Mathar, Aug 09 2010

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