A298018 Partial sums of A298015.

1, 4, 10, 25, 49, 67, 100, 148, 178, 229, 301, 343, 412, 508, 562, 649, 769, 835, 940, 1084, 1162, 1285, 1453, 1543, 1684, 1876, 1978, 2137, 2353, 2467, 2644, 2884, 3010, 3205, 3469, 3607, 3820, 4108, 4258, 4489, 4801, 4963, 5212, 5548, 5722, 5989, 6349, 6535, 6820, 7204, 7402, 7705, 8113, 8323

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. A298015.

Programs

Mathematica

LinearRecurrence[{1,0,2,-2,0,-1,1},{1,4,10,25,49,67,100,148},60] (* Harvey P. Dale, Apr 30 2023 *)

PARI

Vec((1 + 3*x + 6*x^2 + 13*x^3 + 18*x^4 + 6*x^5 + 4*x^6 + 3*x^7) / ((1 - x)^3*(1 + x + x^2)^2) + O(x^50)) \\ Colin Barker, Jan 15 2018

Formula

From Colin Barker, Jan 15 2018: (Start)

G.f.: (1 + 3*x + 6*x^2 + 13*x^3 + 18*x^4 + 6*x^5 + 4*x^6 + 3*x^7) / ((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>7.

(End)