A299280 Partial sums of A299279.

1, 9, 39, 107, 233, 413, 699, 1047, 1557, 2129, 2927, 3779, 4929, 6117, 7683, 9263, 11309, 13337, 15927, 18459, 21657, 24749, 28619, 32327, 36933, 41313, 46719, 51827, 58097, 63989, 71187, 77919, 86109, 93737, 102983, 111563, 121929, 131517, 143067, 153719, 166517

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Formula

From Colin Barker, Feb 11 2018: (Start)

G.f.: (1 + 8*x + 27*x^2 + 44*x^3 + 39*x^4 - 3*x^6 + 4*x^7) / ((1 - x)^4*(1 + x)^3).

a(n) = (5*n^3 + 8*n^2 + 6*n - 6) / 2 for n>0 and even.

a(n) = (5*n^3 + 7*n^2 + 5*n + 1) / 2 for n odd.

a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7) for n>7.

(End)

Mathematica

LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 9, 39, 107, 233, 413, 699, 1047}, 50] (* Harvey P. Dale, Jul 22 2021 *)

Prog

(PARI) Vec((1 + 8*x + 27*x^2 + 44*x^3 + 39*x^4 - 3*x^6 + 4*x^7) / ((1 - x)^4*(1 + x)^3) + O(x^60)) \\ Colin Barker, Feb 11 2018

Crossrefs

Cf. A299279.

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: A158447 A281381 A226449 * A023163 A054121 A139594

Adjacent sequences: A299277 A299278 A299279 * A299281 A299282 A299283

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 10 2018

Status

approved