A301302 Partial sums of A301301.

1, 5, 13, 25, 41, 61, 86, 116, 150, 189, 232, 279, 332, 388, 448, 513, 581, 656, 734, 815, 902, 991, 1088, 1188, 1290, 1399, 1509, 1628, 1750, 1873, 2004, 2135, 2276, 2420, 2564, 2717, 2869, 3032, 3198, 3363, 3538, 3711, 3896, 4084, 4270, 4467, 4661, 4868, 5078, 5285, 5504

Offset: 0

Author

N. J. A. Sloane, Mar 25 2018

Keywords

• nonn
• easy

Comments

Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301301. - Ray Chandler, Aug 31 2023

Links

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

Crossrefs

Cf. A301301.

Programs

Mathematica

LinearRecurrence[{1, 0, 0, 0, 2, -2, 0, 0, 0, -1, 1},{1,5,13,25,41,61,86,116,150,189,232,279,332,388,448,513,581,656},51] (* Stefano Spezia, Mar 11 2025 *)

Formula

From Colin Barker, Apr 07 2018: (Start)

G.f.: (1 + x)^2*(1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 4*x^5 + 4*x^6 + 2*x^7 + 2*x^8 + x^9 + x^12 - 2*x^13 + x^14 - x^15) / ((1 - x)^3*(1 + x + x^2 + x^3 + x^4)^2).

a(n) = a(n-1) + 2*a(n-5) - 2*a(n-6) - a(n-10) + a(n-11) for n>12. (End)

a(n) ~ 54n^2/25. - Stefano Spezia, Mar 11 2025