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A299261 Partial sums of A299255. 51
1, 8, 31, 81, 168, 303, 497, 760, 1103, 1537, 2072, 2719, 3489, 4392, 5439, 6641, 8008, 9551, 11281, 13208, 15343, 17697, 20280, 23103, 26177, 29512, 33119, 37009, 41192, 45679, 50481, 55608, 61071, 66881, 73048, 79583, 86497, 93800, 101503, 109617 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Euler transform of length 3 sequence [8, -5, 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,-3,2,-3,3,-1).

FORMULA

From Colin Barker, Feb 09 2018: (Start)

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

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

(End)

a(n) = -a(-1-n) for all n in Z. - Michael Somos, Oct 03 2018

MATHEMATICA

a[ n_] := (8 (2 n + 1) (n^2 + n + 1) - Mod[n - 1, 3, -1]) / 9; (* Michael Somos, Oct 03 2018 *)

PROG

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

(PARI) {a(n) =  (8 * (2*n + 1) * (n^2 + n + 1) + (n%3==0) - (n%3==2)) / 9}; /* Michael Somos, Oct 03 2018 */

CROSSREFS

Cf. A299255.

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: A212579 A115004 A303522 * A005338 A006322 A319906

Adjacent sequences:  A299258 A299259 A299260 * A299262 A299263 A299264

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 07 2018

STATUS

approved

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Last modified November 16 23:51 EST 2018. Contains 317275 sequences. (Running on oeis4.)