A301723 Partial sums of A301722.

1, 6, 16, 31, 53, 80, 111, 149, 192, 239, 293, 352, 415, 485, 560, 639, 725, 816, 911, 1013, 1120, 1231, 1349, 1472, 1599, 1733, 1872, 2015, 2165, 2320, 2479, 2645, 2816, 2991, 3173, 3360, 3551, 3749, 3952, 4159, 4373, 4592, 4815, 5045, 5280, 5519, 5765, 6016, 6271

Offset: 0

Author

N. J. A. Sloane, Mar 26 2018

Keywords

• nonn

Comments

Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301722. - Ray Chandler, Aug 30 2023

Links

• Ray Chandler, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2, -1, 1, -2, 1).

Crossrefs

Cf. A301722.

Programs

Mathematica

LinearRecurrence[{2,-1,1,-2,1},{1,6,16,31,53,80,111},50] (* Harvey P. Dale, Aug 18 2025 *)

Formula

From Colin Barker, Apr 06 2018: (Start)

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

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5) for n>4.

(End)