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 A299265 Partial sums of A299259. 51
 1, 6, 19, 45, 90, 159, 257, 390, 563, 781, 1050, 1375, 1761, 2214, 2739, 3341, 4026, 4799, 5665, 6630, 7699, 8877, 10170, 11583, 13121, 14790, 16595, 18541, 20634, 22879, 25281, 27846, 30579, 33485, 36570, 39839, 43297, 46950, 50803, 54861, 59130 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Euler transform of length 4 sequence [6, -2, 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,-3,2,-3,3,-1). FORMULA From Colin Barker, Feb 09 2018: (Start) G.f.: (1 + x)^3*(1 + x^2) / ((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) a(n) = -a(-1-n) for all n in Z. - Michael Somos, Oct 03 2018 MATHEMATICA CoefficientList[Series[(1+x)^3*(1+x^2)/((1-x)^4*(1+x+x^2)), {x, 0, 50}], x] (* G. C. Greubel, Feb 20 2018 *) a[ n_] := (8 n^3 + 12 n^2 + 24 n + 9 + Mod[n, 3]) / 9; (* Michael Somos, Oct 03 2018 *) LinearRecurrence[{3, -3, 2, -3, 3, -1}, {1, 6, 19, 45, 90, 159}, 50] (* Harvey P. Dale, Dec 11 2018 *) PROG (PARI) Vec((1 + x)^3*(1 + x^2) / ((1 - x)^4*(1 + x + x^2)) + O(x^60)) \\ Colin Barker, Feb 09 2018 (PARI) {a(n) =  (8*n^3 + 12*n^2 + 24*n + 9 + (n%3)) / 9}; /* Michael Somos, Oct 03 2018 */ (MAGMA) I:=[19, 45, 90, 159, 257, 390]; [1, 6] cat [n le 6 select I[n] else 3*Self(n-1) - 3*Self(n-2) +2*Self(n-3) - 3*Self(n-4) + 3*Self(n-5) - Self(n-6): n in [1..30]]; CROSSREFS Cf. A299259. 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: A209403 A272707 A266938 * A005712 A299278 A298741 Adjacent sequences:  A299262 A299263 A299264 * A299266 A299267 A299268 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Feb 07 2018 STATUS approved

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Last modified February 16 15:55 EST 2020. Contains 331961 sequences. (Running on oeis4.)