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

Offset: 0

Author

Stefano Spezia, Oct 26 2022

Keywords

• nonn
• easy

Links

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

Crossrefs

Partial sums of the main diagonal of A143976.

Cf. A042968 (2nd differences), A071619 (1st differences).

Cf. A005898, A049347.

Programs

Mathematica

LinearRecurrence[{3,-3,2,-3,3,-1},{0,1,4,10,21,38},47]

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.