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

0,2

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).

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)

Mathematica

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

Prog

(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

Crossrefs

Cf. A298015.

Sequence in context: A145368 A266826 A111207 * A254233 A300760 A347481

Adjacent sequences: A298015 A298016 A298017 * A298019 A298020 A298021

Keyword

nonn,easy

Author

Chaim Goodman-Strauss and N. J. A. Sloane, Jan 13 2018

Status

approved