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

0,2

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).

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)

Prog

(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

Crossrefs

Cf. A087960, A301291.

Sequence in context: A000384 A164000 A212087 * A359696 A134978 A115742

Adjacent sequences: A301289 A301290 A301291 * A301293 A301294 A301295

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 23 2018

Status

approved