A365205 Centered pentachoral numbers.

1, 21, 121, 421, 1101, 2401, 4621, 8121, 13321, 20701, 30801, 44221, 61621, 83721, 111301, 145201, 186321, 235621, 294121, 362901, 443101, 535921, 642621, 764521, 903001, 1059501, 1235521, 1432621, 1652421, 1896601, 2166901, 2465121, 2793121, 3152821

Offset

1,2

Comments

A pentachoral number is a centered figurate number that represents a pentachoron, which is a four-dimensional regular polytope composed of 5 cells.

One of the 6 centered regular polichoral (centered pentachoral, centered hexadecachoral, centered octachoral, centered icositetrachoral, centered hexacosichoral and centered hecatonicosachoral) numbers.

Links

Table of n, a(n) for n=1..34.

Eric Weisstein's World of Mathematics, Figurate Number.

Wikipedia, 5-cell.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = 5*n^4/2 - 5*n^3 + 15*n^2/2 - 5*n + 1.

G.f.: x*(1 + 16*x + 26*x^2 + 16*x^3 + x^4)/(1 - x)^5. - Stefano Spezia, Aug 26 2023

Mathematica

Table[5/2*n^4 - 5*n^3 + 15/2*n^2 - 5*n + 1, {n, 1, 100}]

Crossrefs

Cf. A005448 (2D), A005898 (3D), A362863, A365204, A365206.

Sequence in context: A044353 A044734 A325484 * A361699 A200888 A179441

Adjacent sequences: A365202 A365203 A365204 * A365206 A365207 A365208

Keyword

nonn,easy

Author

Léo Cymrot Cymbalista, Aug 25 2023

Status

approved