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A299267
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Partial sums of A299266.
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51
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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
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2,-2,3,-2,0,0,-2,3,-2,2,-1).
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FORMULA
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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)
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MATHEMATICA
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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 *)
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PROG
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(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
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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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