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A063489
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a(n) = (2*n-1)*(5*n^2-5*n+6)/6.
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65
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1, 8, 30, 77, 159, 286, 468, 715, 1037, 1444, 1946, 2553, 3275, 4122, 5104, 6231, 7513, 8960, 10582, 12389, 14391, 16598, 19020, 21667, 24549, 27676, 31058, 34705, 38627, 42834, 47336, 52143, 57265, 62712, 68494, 74621, 81103, 87950
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: x*(1+x)*(1+3*x+x^2)/(1-x)^4. - Colin Barker, Mar 02 2012
a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4), with a(1)=1, a(2)=8, a(3)=30, a(4)=77. - Harvey P. Dale, Aug 20 2012
E.g.f.: (-6 + 12*x + 15*x^2 + 10*x^3)*exp(x)/6 + 1. - G. C. Greubel, Dec 01 2017
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MATHEMATICA
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Table[(2n-1)(5n^2-5n+6)/6, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 8, 30, 77}, 40] (* Harvey P. Dale, Aug 20 2012 *)
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PROG
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(PARI) { for (n=1, 1000, write("b063489.txt", n, " ", (2*n - 1)*(5*n^2 - 5*n + 6)/6) ) } \\ Harry J. Smith, Aug 23 2009
(Magma) [(2*n-1)*(5*n^2-5*n+6)/6: n in [1..30]]; // G. C. Greubel, Dec 01 2017
(PARI) x='x+O('x^30); Vec(serlaplace((-6 + 12*x + 15*x^2 + 10*x^3 )*exp(x)/6 + 1)) \\ G. C. Greubel, Dec 01 2017
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CROSSREFS
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1/12*t*(2*n^3-3*n^2+n)+2*n-1 for t = 2, 4, 6, ... gives A049480, A005894, A063488, A001845, A063489, A005898, A063490, A057813, A063491, A005902, A063492, A005917, A063493, A063494, A063495, A063496.
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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