The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A299264 Partial sums of A299258. 51
 1, 6, 19, 44, 85, 147, 236, 357, 514, 711, 953, 1246, 1595, 2004, 2477, 3019, 3636, 4333, 5114, 5983, 6945, 8006, 9171, 10444, 11829, 13331, 14956, 16709, 18594, 20615, 22777, 25086, 27547, 30164, 32941, 35883, 38996, 42285, 45754, 49407, 53249, 57286, 61523 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Euler transform of length 6 sequence [6, -2, 0, 0, 1, -1]. - Michael Somos, Oct 03 2018 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,1,-3,3,-1). FORMULA From Colin Barker, Feb 09 2018: (Start) G.f.: (1 + x)^3*(1 - x + x^2)*(1 + x + x^2) / ((1 - x)^4*(1 + x + x^2 + x^3 + x^4)). a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-5) - 3*a(n-6) + 3*a(n-7) - a(n-8) for n>7. (End) a(n) = -a(-1-n) for all n in Z. - Michael Somos, Oct 03 2018 EXAMPLE G.f. = 1 + 6*x + 19*x^2 + 44*x^3 + 85*x^4 + 147*x^5 + 236*x^6 + ... - Michael Somos, Oct 03 2018 MATHEMATICA a[ n_] := (4 n^3 + 6 n^2 + 16 n + {5, 4, 7, 10, 9}[[Mod[n, 5] + 1]]) / 5; (* Michael Somos, Oct 03 2018 *) PROG (PARI) Vec((1 + x)^3*(1 - x + x^2)*(1 + x + x^2) / ((1 - x)^4*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ Colin Barker, Feb 09 2018 (PARI) {a(n) = (4*n^3 + 6*n^2 + 16*n + [5, 4, 7, 10, 9][n%5+1]) / 5}; /* Michael Somos, Oct 03 2018 */ CROSSREFS Cf. A299258. 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: A061293 A005900 A138357 * A183763 A209403 A272707 Adjacent sequences:  A299261 A299262 A299263 * A299265 A299266 A299267 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Feb 07 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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