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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
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: A272707 A266938 A362602 * A005712 A299278 A298741
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 07 2018
STATUS
approved

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Last modified March 28 15:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)