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A358042

Partial sums of A071619.

0, 1, 4, 10, 21, 38, 62, 95, 138, 192, 259, 340, 436, 549, 680, 830, 1001, 1194, 1410, 1651, 1918, 2212, 2535, 2888, 3272, 3689, 4140, 4626, 5149, 5710, 6310, 6951, 7634, 8360, 9131, 9948, 10812, 11725, 12688, 13702, 14769, 15890, 17066, 18299, 19590, 20940, 22351

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..46.

Index entries for linear recurrences with constant coefficients, signature (3,-3,2,-3,3,-1).

FORMULA

O.g.f.: x*(1 + x)*(1 + x^2)/((1 + x + x^2)*(1 - x)^4).

a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6) for n > 5.

a(n) = (A005898(n) - A049347(n))/9.

E.g.f.: exp(-x/2)*(3*exp(3*x/2)*(1 + 8*x + 9*x^2 + 2*x^3) - 3*cos(sqrt(3)*x/2) - sqrt(3)*sin(sqrt(3)*x/2))/27.

MATHEMATICA