A364429 a(0) = 1, a(n) = (2*n^5 + 20*n^3 + 23*n) * 2/15 for n>=1.

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

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