A299260 Partial sums of A299254.

1, 8, 29, 74, 153, 275, 450, 687, 996, 1387, 1869, 2452, 3145, 3958, 4901, 5983, 7214, 8603, 10160, 11895, 13817, 15936, 18261, 20802, 23569, 26571, 29818, 33319, 37084, 41123, 45445, 50060, 54977, 60206, 65757, 71639, 77862, 84435, 91368, 98671, 106353

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,1,-3,3,-1).

Formula

From Colin Barker, Feb 09 2018: (Start)

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

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

(End)

a(n) = (1/5)*(8*n^3 + 12*n^2 + 14*n + 5 + [n == 1 (mod 5)] - [n == 3 (mod 5)]). - Eric Simon Jacob, Feb 14 2023

Prog

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

Crossrefs

Cf. A299254.

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: A100178 A106113 A362153 * A290312 A028419 A046664

Adjacent sequences: A299257 A299258 A299259 * A299261 A299262 A299263

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 07 2018

Status

approved