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

0,2

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).

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)

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 *)

Crossrefs

Cf. A301289.

Sequence in context: A194275 A026059 A115002 * A152234 A357997 A054514

Adjacent sequences: A301287 A301288 A301289 * A301291 A301292 A301293

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 23 2018

Status

approved