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 A299267 Partial sums of A299266. 51
 1, 6, 15, 37, 74, 131, 213, 330, 475, 653, 882, 1163, 1485, 1862, 2307, 2821, 3398, 4043, 4773, 5598, 6499, 7481, 8574, 9779, 11073, 12470, 13995, 15649, 17414, 19295, 21321, 23502, 25807, 28241, 30846, 33623, 36537, 39602, 42855, 46297, 49898, 53663, 57633, 61818, 66175, 70709, 75474, 80471, 85653, 91034, 96663 (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 (2,-2,3,-2,0,0,-2,3,-2,2,-1). FORMULA From Colin Barker, Feb 15 2018: (Start) G.f.: (1 +4*x +5*x^2 +16*x^3 +14*x^4 +24*x^5 +18*x^6 +20*x^7 +5*x^8 + x^10 -4*x^11 +4*x^12)/((1 -x)^4*(1 +x)*(1 +x^2)^2*(1 +x +x^2)). a(n) = 2*a(n-1) - 2*a(n-2) + 3*a(n-3) - 2*a(n-4) - 2*a(n-7) + 3*a(n-8) - 2*a(n-9) + 2*a(n-10) - a(n-11) for n>12. (End) MATHEMATICA CoefficientList[Series[(1 +4*x +5*x^2 +16*x^3 +14*x^4 +24*x^5 +18*x^6 +20*x^7 +5*x^8 + x^10 -4*x^11 +4*x^12)/((1 -x)^4*(1 +x)*(1 +x^2)^2*(1 +x +x^2)), {x, 0, 50}], x] (* G. C. Greubel, Feb 20 2018 *) LinearRecurrence[{2, -2, 3, -2, 0, 0, -2, 3, -2, 2, -1}, {1, 6, 15, 37, 74, 131, 213, 330, 475, 653, 882, 1163, 1485}, 60] (* Harvey P. Dale, Sep 03 2018 *) PROG (PARI) Vec((1 + 4*x + 5*x^2 + 16*x^3 + 14*x^4 + 24*x^5 + 18*x^6 + 20*x^7 + 5*x^8 + x^10 - 4*x^11 + 4*x^12) / ((1 - x)^4*(1 + x)*(1 + x^2)^2*(1 + x + x^2)) + O(x^60)) \\ Colin Barker, Feb 15 2018 (MAGMA) I:=[15, 37, 74, 131, 213, 330, 475, 653, 882, 1163, 1485]; [1, 6] cat [n le 11 select I[n] else 2*Self(n-1) -2*Self(n-2) +3*Self(n-3)-2*Self(n-4)-2*Self(n-7) +3*Self(n-8) -2*Self(n-9)+2*Self(n-10)-Self(n-11): n in [1..30]]; // G. C. Greubel, Feb 20 2018 CROSSREFS Cf. A299266. 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: A135854 A221905 A083011 * A254008 A277089 A271545 Adjacent sequences:  A299264 A299265 A299266 * A299268 A299269 A299270 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Feb 07 2018 STATUS approved

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Last modified January 24 19:12 EST 2021. Contains 340411 sequences. (Running on oeis4.)