A301290 Partial sums of A301289.

1, 5, 10, 16, 28, 42, 57, 75, 96, 122, 150, 176, 207, 245, 282, 320, 364, 410, 457, 507, 560, 618, 678, 736, 799, 869, 938, 1008, 1084, 1162, 1241, 1323, 1408, 1498, 1590, 1680, 1775, 1877, 1978, 2080, 2188, 2298, 2409, 2523, 2640, 2762, 2886, 3008, 3135, 3269, 3402, 3536

Offset: 0

Author

N. J. A. Sloane, Mar 23 2018

Keywords

• nonn
• easy

Comments

Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301289. - 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 (3,-5,7,-8,8,-7,5,-3,1).

Crossrefs

Cf. A301289.

Programs

Mathematica

Accumulate[LinearRecurrence[{2,-3,4,-4,4,-3,2,-1},{1,4,5,6,12,14,15,18,21,26},100]] (* Harvey P. Dale, Jun 21 2024 *)

Formula

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

a(n) = 3*a(n-1) - 5*a(n-2) + 7*a(n-3) - 8*a(n-4) + 8*a(n-5) - 7*a(n-6) + 5*a(n-7) - 3*a(n-8) + a(n-9) for n > 9.

G.f.: (2*x^9 - 6*x^8 + 4*x^7 - 6*x^6 - 3*x^4 - 4*x^3 - 2*x - 1)/((x - 1)^3*(x^2 + 1)*(x^2 - x + 1)*(x^2 + x + 1)). (End)