A298019 Partial sums of A298016.

1, 7, 19, 31, 55, 91, 115, 157, 217, 253, 313, 397, 445, 523, 631, 691, 787, 919, 991, 1105, 1261, 1345, 1477, 1657, 1753, 1903, 2107, 2215, 2383, 2611, 2731, 2917, 3169, 3301, 3505, 3781, 3925, 4147, 4447, 4603, 4843, 5167, 5335, 5593, 5941, 6121, 6397, 6769, 6961, 7255, 7651, 7855, 8167, 8587

Offset: 0

Author

Chaim Goodman-Strauss and N. J. A. Sloane, Jan 13 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 (1,0,2,-2,0,-1,1).

Crossrefs

Cf. A298016.

Programs

PARI

Vec((1 + 6*x + 12*x^2 + 10*x^3 + 12*x^4 + 12*x^5 + x^6) / ((1 - x)^3*(1 + x + x^2)^2) + O(x^80)) \\ Colin Barker, Jan 16 2018

Formula

From Colin Barker, Jan 16 2018: (Start)

G.f.: (1 + 6*x + 12*x^2 + 10*x^3 + 12*x^4 + 12*x^5 + x^6) / ((1 - x)^3*(1 + x + x^2)^2).

a(n) = a(n-1) + 2*a(n-3) - 2*a(n-4) - a(n-6) + a(n-7) for n>6.

(End)