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a(0) = 1, a(n) = (2*n^5 + 20*n^3 + 23*n) * 2/15 for n>=1.
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%I #23 Jul 28 2024 03:48:48

%S 1,6,36,146,456,1182,2668,5418,10128,17718,29364,46530,71000,104910,

%T 150780,211546,290592,391782,519492,678642,874728,1113854,1402764,

%U 1748874,2160304,2645910,3215316,3878946,4648056,5534766,6552092,7713978,9035328,10532038,12221028

%N a(0) = 1, a(n) = (2*n^5 + 20*n^3 + 23*n) * 2/15 for n>=1.

%C a(n) is the 6th n-orthoplex (n-dimensional cross-polytope) number.

%H OEIS Wiki, <a href="https://oeis.org/wiki/Orthoplex_numbers">Orthoplex numbers</a>.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F a(0) = 1, a(n) = (2*n^5 + 20*n^3 + 23*n) * 2/15 for n>=1.

%F G.f.: (1 + 15*x^2 + 15*x^4 + x^6)/(1 - x)^6. - _Stefano Spezia_, Jul 24 2023

%e a(3) = 146 since the 6th octahedral number is 146; A005900(6) = 146.

%e a(4) = 456 since the 6th 16-cell number is 456; A014820(5) = 456.

%t Prepend[Table[2/15 (2 x^5 + 20 x^3 + 23 x), {x, 100}], 1]

%o (Python)

%o print([1]+[(2*i**5+20*i**3+23*i)*2//15 for i in range(1,101)])

%Y Cf. A005900, A014820, A069038, A069039, A099193, A099195, A099196, A099197, A058331.

%Y Cf. A142978 (column 6 with an initial 1).

%K nonn,easy

%O 0,2

%A _Steven Lu_, Jul 24 2023