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A299280
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Partial sums of A299279.
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51
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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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).
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FORMULA
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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)
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MATHEMATICA
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LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 9, 39, 107, 233, 413, 699, 1047}, 50] (* Harvey P. Dale, Jul 22 2021 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Feb 10 2018
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STATUS
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approved
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