A299264 Partial sums of A299258.

1, 6, 19, 44, 85, 147, 236, 357, 514, 711, 953, 1246, 1595, 2004, 2477, 3019, 3636, 4333, 5114, 5983, 6945, 8006, 9171, 10444, 11829, 13331, 14956, 16709, 18594, 20615, 22777, 25086, 27547, 30164, 32941, 35883, 38996, 42285, 45754, 49407, 53249, 57286, 61523

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.

Sequence in context: A061293 A005900 A138357 * A183763 A209403 A272707

Adjacent sequences: A299261 A299262 A299263 * A299265 A299266 A299267

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 07 2018

Status

approved