A301292 Partial sums of A301291.

1, 6, 15, 28, 46, 69, 96, 127, 163, 204, 249, 298, 352, 411, 474, 541, 613, 690, 771, 856, 946, 1041, 1140, 1243, 1351, 1464, 1581, 1702, 1828, 1959, 2094, 2233, 2377, 2526, 2679, 2836, 2998, 3165, 3336, 3511, 3691, 3876, 4065, 4258, 4456, 4659

Offset: 0

Author

N. J. A. Sloane, Mar 23 2018

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-3,1).

Crossrefs

Cf. A087960, A301291.

Programs

PARI

Vec((1 + 3*x + x^2 + 3*x^3 + x^4) / ((1 - x)^3*(1 + x^2)) + O(x^60)) \\ Colin Barker, Mar 23 2018

Formula

From Colin Barker, Mar 23 2018: (Start)

G.f.: (1 + 3*x + x^2 + 3*x^3 + x^4)/((1 - x)^3*(1 + x^2)).

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

(End)

From Stefano Spezia, Jan 30 2023: (Start)

a(n) = (5 + 9*n*(1 + n) - A087960(n))/4.

E.g.f.: (exp(x)*(5 + 18*x + 9*x^2) - cos(x) + sin(x))/4. (End)