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A299276 Partial sums of A008137. 51
1, 5, 14, 31, 59, 101, 161, 242, 347, 479, 641, 837, 1070, 1343, 1659, 2021, 2433, 2898, 3419, 3999, 4641, 5349, 6126, 6975, 7899, 8901, 9985, 11154, 12411, 13759, 15201, 16741, 18382, 20127, 21979, 23941, 26017, 28210, 30523, 32959, 35521, 38213, 41038 (list; graph; refs; listen; history; text; internal format)
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

From Colin 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 in A299266 for overview.

Sequence in context: A070129 A081861 A299903 * A267167 A023652 A283523

Adjacent sequences:  A299273 A299274 A299275 * A299277 A299278 A299279

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 10 2018

STATUS

approved

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