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 A364429 a(0) = 1, a(n) = (2*n^5 + 20*n^3 + 23*n) * 2/15 for n>=1. 0
 1, 6, 36, 146, 456, 1182, 2668, 5418, 10128, 17718, 29364, 46530, 71000, 104910, 150780, 211546, 290592, 391782, 519492, 678642, 874728, 1113854, 1402764, 1748874, 2160304, 2645910, 3215316, 3878946, 4648056, 5534766, 6552092, 7713978, 9035328, 10532038, 12221028 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is the 6th n-orthoplex (n-dimensional cross-polytope) number. LINKS Table of n, a(n) for n=0..34. OEIS Wiki, Orthoplex numbers. Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA a(0) = 1, a(n) = (2*n^5 + 20*n^3 + 23*n) * 2/15 for n>=1. G.f.: (1 + 15*x^2 + 15*x^4 + x^6)/(1 - x)^6. - Stefano Spezia, Jul 24 2023 EXAMPLE a(3) = 146 since the 6th octahedral number is 146; A005900(6) = 146. a(4) = 456 since the 6th 16-cell number is 456; A014820(5) = 456. MATHEMATICA Prepend[Table[2/15 (2 x^5 + 20 x^3 + 23 x), {x, 100}], 1] PROG (Python) print([1]+[(2*i**5+20*i**3+23*i)*2//15 for i in range(1, 101)]) CROSSREFS Cf. A005900, A014820, A069038, A069039, A099193, A099195, A099196, A099197, A058331. Cf. A142978 (column 6 with an initial 1). Sequence in context: A056375 A360588 A321579 * A018214 A181478 A223841 Adjacent sequences: A364426 A364427 A364428 * A364430 A364431 A364432 KEYWORD nonn,easy AUTHOR Steven Lu, Jul 24 2023 STATUS approved

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Last modified September 9 06:26 EDT 2024. Contains 375759 sequences. (Running on oeis4.)