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

0,2

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).

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

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 *)

Crossrefs

Cf. A301301.

Sequence in context: A380280 A001844 A099776 * A133322 A299258 A301671

Adjacent sequences: A301299 A301300 A301301 * A301303 A301304 A301305

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 25 2018

Status

approved