A299263 Partial sums of A299257.

1, 6, 18, 40, 76, 132, 214, 325, 469, 652, 878, 1150, 1474, 1856, 2298, 2803, 3379, 4032, 4762, 5572, 6472, 7468, 8558, 9745, 11041, 12452, 13974, 15610, 17374, 19272, 21298, 23455, 25759, 28216, 30818, 33568, 36484, 39572, 42822, 46237, 49837, 53628, 57598

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-8,12,-14,12,-8,4,-1).

Formula

From Colin Barker, Feb 09 2018: (Start)

G.f.: (1 + x)*(1 + x + x^2 + 3*x^3 - x^4 + 5*x^5 - 3*x^6 + 4*x^7 - 2*x^8) / ((1 - x)^4*(1 + x^2)^2).

a(n) = 4*a(n-1) - 8*a(n-2) + 12*a(n-3) - 14*a(n-4) + 12*a(n-5) - 8*a(n-6) + 4*a(n-7) - a(n-8) for n>8.

(End)

5*a(n) = 2*(2*n+1)*(2*n^2+2*n+9)/3 - A138019(n). - R. J. Mathar, Feb 12 2021

Prog

(PARI) Vec((1 + x)*(1 + x + x^2 + 3*x^3 - x^4 + 5*x^5 - 3*x^6 + 4*x^7 - 2*x^8) / ((1 - x)^4*(1 + x^2)^2) + O(x^60)) \\ Colin Barker, Feb 09 2018

Crossrefs

Cf. A299257.

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.

Sequence in context: A002411 A023658 A059834 * A374339 A015224 A163983

Adjacent sequences: A299260 A299261 A299262 * A299264 A299265 A299266

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 07 2018

Status

approved