A298787 Partial sums of A298786.

1, 4, 11, 21, 34, 51, 71, 94, 121, 151, 184, 221, 261, 304, 351, 401, 454, 511, 571, 634, 701, 771, 844, 921, 1001, 1084, 1171, 1261, 1354, 1451, 1551, 1654, 1761, 1871, 1984, 2101, 2221, 2344, 2471, 2601, 2734, 2871, 3011, 3154, 3301, 3451, 3604, 3761, 3921, 4084, 4251, 4421, 4594, 4771

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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

Formula

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

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5) for n>4. - Colin Barker, Jan 27 2018

From Stefano Spezia, Apr 06 2023: (Start)

a(n) = (8 + 15*n + 15*n^2 + A061347(n+2))/9.

E.g.f.: exp(-x/2)*(exp(3*x/2)*(8 + 30*x + 15*x^2 + cos(sqrt(3)*x/2) - sqrt(3)*sin(sqrt(3)*x/2))/9. (End]

Prog

(PARI) Vec((1 + 2*x + 4*x^2 + 2*x^3 + x^4) / ((1 - x)^3*(1 + x + x^2)) + O(x^60)) \\ Colin Barker, Jan 27 2018

Crossrefs

Cf. A061347, A298786.

Sequence in context: A323625 A301096 A115067 * A009893 A027369 A301111

Adjacent sequences: A298784 A298785 A298786 * A298788 A298789 A298790

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 26 2018

Status

approved