A301685 Partial sums of A301684.

1, 5, 13, 25, 43, 65, 93, 127, 163, 205, 253, 303, 359, 421, 485, 555, 631, 709, 793, 883, 975, 1073, 1177, 1283, 1395, 1513, 1633, 1759, 1891, 2025, 2165, 2311, 2459, 2613, 2773, 2935, 3103, 3277, 3453, 3635, 3823, 4013, 4209, 4411, 4615, 4825, 5041, 5259, 5483, 5713, 5945, 6183, 6427, 6673, 6925, 7183, 7443, 7709, 7981

Offset

0,2

Comments

Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301684. - 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).

Formula

From Chai Wah Wu, Feb 03 2021: (Start)

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5) for n > 8.

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

Mathematica

LinearRecurrence[{2, -1, 1, -2, 1}, {1, 5, 13, 25, 43, 65, 93, 127, 163}, 60] (* Harvey P. Dale, Jun 22 2024 *)

Crossrefs

Cf. A301684.

Sequence in context: A241233 A064276 A240001 * A102724 A147031 A147220

Adjacent sequences: A301682 A301683 A301684 * A301686 A301687 A301688

Keyword

nonn

Author

N. J. A. Sloane, Mar 25 2018

Status

approved