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 A299269 Partial sums of A299268. 51
 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 (list; graph; refs; listen; history; text; internal format)
 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 09 2018: (Start) 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) MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A299268. 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: A155291 A155221 A213569 * A048477 A294837 A117152 Adjacent sequences:  A299266 A299267 A299268 * A299270 A299271 A299272 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Feb 07 2018 STATUS approved

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Last modified February 26 12:33 EST 2020. Contains 332279 sequences. (Running on oeis4.)