OFFSET
0,2
COMMENTS
Euler transform of length 6 sequence [5, -1, 1, -1, 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
FromColin Barker, Feb 11 2018: (Start)
G.f.: (1 + x)^3*(1 - x + x^2)*(1 + 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.
EXAMPLE
G.f. = 1 + 5*x + 14*x^2 + 31*x^3 + 59*x^4 + 101*x^5 + 161*x^6 + ... -Michael Somos, Oct 03 2018
MATHEMATICA
a[ n_] := (8 n^3 + 12 n^2 + 40 n + 18 - {3, 3, 0, -3, -3, 3}[[Mod[n, 5] + 1]]) / 15; (*Michael Somos, Oct 03 2018 *)
PROG
(PARI) Vec((1 + x)^3*(1 - x + x^2)*(1 + x^2) / ((1 - x)^4*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\Colin Barker, Feb 11 2018
(PARI) {a(n) = (8*n^3 + 12*n^2 + 40*n + 18 - 3*(n%5<2) + 3*(n%5>2)) / 15}; /*Michael Somos, Oct 03 2018 */
CROSSREFS
Cf.A008137.
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 inA299266 for overview.
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 10 2018
STATUS
approved