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A299269
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Partial sums of A299268.
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51
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1, 7, 25, 73, 151, 277, 459, 699, 1029, 1419, 1941, 2517, 3275, 4073, 5111, 6167, 7529, 8879, 10609, 12289, 14431, 16477, 19075, 21523, 24621, 27507, 31149, 34509, 38739, 42609, 47471, 51887, 57425, 62423, 68681, 74297, 81319, 87589, 95419, 102379, 111061
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1 + 6*x + 15*x^2 + 30*x^3 + 27*x^4 + x^6) / ((1 - x)^4*(1 + x)^3).
a(n) = (20*n^3 + 33*n^2 - 2*n + 12) / 12 for n even.
a(n) = (20*n^3 + 27*n^2 + 28*n + 9) / 12 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>6. (End)
E.g.f.: ((12 + 75*x + 93*x^2 + 20*x^3)*cosh(x) + (9 + 51*x + 87*x^2 + 20*x^3)*sinh(x))/12. - Stefano Spezia, Mar 14 2024
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MATHEMATICA
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CoefficientList[Series[(1+6*x+15*x^2+30*x^3+27*x^4+x^6)/((1-x)^4*(1+ x)^3), {x, 0, 50}], x] (* G. C. Greubel, Feb 20 2018 *)
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PROG
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(PARI) Vec((1 + 6*x + 15*x^2 + 30*x^3 + 27*x^4 + x^6) / ((1 - x)^4*(1 + x)^3) + O(x^60)) \\ Colin Barker, Feb 09 2018
(Magma) I:=[25, 73, 151, 277, 459, 699, 1029]; [1, 7] cat [n le 7 select I[n] else Self(n-1) + 3*Self(n-2) - 3*Self(n-3) - 3*Self(n-4) + 3*Self(n-5) + Self(n-6) - Self(n-7): n in [1..30]]; // G. C. Greubel, Feb 20 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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