A301713 Partial sums of A301712.

1, 6, 16, 32, 54, 81, 114, 152, 195, 244, 297, 356, 421, 491, 568, 649, 735, 827, 923, 1026, 1134, 1247, 1367, 1491, 1621, 1756, 1895, 2041, 2192, 2349, 2512, 2679, 2852, 3030, 3213, 3402, 3596, 3796, 4002, 4213, 4429, 4650, 4876, 5108, 5346, 5589, 5838, 6092, 6351, 6616, 6885

Offset

0,2

Comments

Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301712. - 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,-1,0,-1,3,-3,1,0,1,-2,1).

Formula

From Colin Barker, Apr 07 2018: (Start)

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

a(n) = 2*a(n-1) - a(n-2) - a(n-4) + 3*a(n-5) - 3*a(n-6) + a(n-7) + a(n-9) - 2*a(n-10) + a(n-11) for n>10. (End)

Mathematica

LinearRecurrence[{2, -1, 0, -1, 3, -3, 1, 0, 1, -2, 1}, {1, 6, 16, 32, 54, 81, 114, 152, 195, 244, 297}, 100] (* Paolo Xausa, Jul 31 2024 *)

Crossrefs

Cf. A301712.

Sequence in context: A296957 A341276 A301698 * A134465 A036488 A131949

Adjacent sequences: A301710 A301711 A301712 * A301714 A301715 A301716

Keyword

nonn

Author

N. J. A. Sloane, Mar 26 2018

Status

approved