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
MATHEMATICA
LinearRecurrence[{3, -3, 1, 0, 1, -3, 3, -1}, {1, 8, 29, 74, 153, 275, 450, 687}, 50] (* Paolo Xausa, Jan 16 2025 *)
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.
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 07 2018
STATUS
approved