A299284 Partial sums of A299283.

1, 8, 30, 78, 162, 292, 478, 731, 1061, 1478, 1992, 2614, 3354, 4222, 5228, 6383, 7697, 9180, 10842, 12694, 14746, 17008, 19490, 22203, 25157, 28362, 31828, 35566, 39586, 43898, 48512, 53439, 58689, 64272, 70198, 76478, 83122, 90140, 97542, 105339, 113541

Offset: 0

Author

N. J. A. Sloane, Feb 10 2018

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1,1,-3,3,-1).

Crossrefs

Cf. A299283.

The 28 uniform 3D tilings: cab: A299266, A299267; crs: A299268, A299269; fcu: A005901, A005902; fee: A299259, A299265; flu-e: A299272, A299273; fst: A299258, A299264; hal: A299274, A299275; hcp: A007899, A007202; hex: A005897, A005898; kag: A299256, A299262; lta: A008137, A299276; pcu: A005899, A001845; pcu-i: A299277, A299278; reo: A299279, A299280; reo-e: A299281, A299282; rho: A008137, A299276; sod: A005893, A005894; sve: A299255, A299261; svh: A299283, A299284; svj: A299254, A299260; svk: A010001, A063489; tca: A299285, A299286; tcd: A299287, A299288; tfs: A005899, A001845; tsi: A299289, A299290; ttw: A299257, A299263; ubt: A299291, A299292; bnn: A007899, A007202. See the Proserpio link in A299266 for overview.

Programs

Mathematica

LinearRecurrence[{3,-3,1,1,-3,3,-1},{1,8,30,78,162,292,478},50] (* Harvey P. Dale, Mar 30 2024 *)

PARI

Vec((1 + 5*x + 9*x^2 + 11*x^3 + 9*x^4 + 5*x^5 + x^6) / ((1 - x)^4*(1 + x)*(1 + x^2)) + O(x^60)) \\ Colin Barker, Feb 11 2018

Formula

From Colin Barker, Feb 11 2018: (Start)

G.f.: (1 + 5*x + 9*x^2 + 11*x^3 + 9*x^4 + 5*x^5 + x^6) / ((1 - x)^4*(1 + x)*(1 + x^2)).

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

(End)