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A299261
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Partial sums of A299255.
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51
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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
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refs;
listen;
history;
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internal format)
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OFFSET
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0,2
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COMMENTS
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Euler transform of length 3 sequence [8, -5, 1]. - Michael Somos, Oct 03 2018
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LINKS
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FORMULA
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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)
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MATHEMATICA
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a[ n_] := (8 (2 n + 1) (n^2 + n + 1) - Mod[n - 1, 3, -1]) / 9; (* Michael Somos, Oct 03 2018 *)
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PROG
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(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 */
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CROSSREFS
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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.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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