A301715 Partial sums of A301714.

1, 6, 18, 34, 55, 83, 114, 152, 196, 243, 299, 358, 422, 494, 567, 649, 736, 826, 926, 1027, 1135, 1250, 1366, 1492, 1621, 1755, 1898, 2042, 2194, 2351, 2511, 2680, 2852, 3030, 3215, 3403, 3598, 3798, 4002, 4213, 4429, 4650, 4878, 5110, 5347, 5591, 5838, 6092, 6352, 6615, 6887, 7162, 7442, 7730, 8019, 8317, 8620

Offset

0,2

Comments

Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301714. - 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 09 2018: (Start)

G.f.: (1 + 4*x + 7*x^2 + 4*x^3 + 6*x^4 + 10*x^5 + 6*x^6 + 4*x^7 + 7*x^8 + 4*x^9+ x^10) / ((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, 18, 34, 55, 83, 114, 152, 196, 243, 299}, 100] (* Paolo Xausa, Jul 31 2024 *)

Crossrefs

Cf. A301714.

Sequence in context: A134078 A323148 A181510 * A269755 A270135 A038343

Adjacent sequences: A301712 A301713 A301714 * A301716 A301717 A301718

Keyword

nonn

Author

N. J. A. Sloane, Mar 26 2018

Status

approved