OFFSET
0,2
COMMENTS
Euler transform of length 6 sequence [6, -2, 0, 0, 1, -1]. - Michael Somos, Oct 03 2018
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)^3*(1 - x + x^2)*(1 + x + x^2) / ((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) = -a(-1-n) for all n in Z. - Michael Somos, Oct 03 2018
a(n) ~ 4*n^3/5. - Stefano Spezia, Jun 06 2024
EXAMPLE
G.f. = 1 + 6*x + 19*x^2 + 44*x^3 + 85*x^4 + 147*x^5 + 236*x^6 + ... - Michael Somos, Oct 03 2018
MATHEMATICA
a[ n_] := (4 n^3 + 6 n^2 + 16 n + {5, 4, 7, 10, 9}[[Mod[n, 5] + 1]]) / 5; (* Michael Somos, Oct 03 2018 *)
PROG
(PARI) Vec((1 + x)^3*(1 - x + x^2)*(1 + x + x^2) / ((1 - x)^4*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ Colin Barker, Feb 09 2018
(PARI) {a(n) = (4*n^3 + 6*n^2 + 16*n + [5, 4, 7, 10, 9][n%5+1]) / 5}; /* Michael Somos, Oct 03 2018 */
CROSSREFS
Cf. A299258.
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