A365204 Centered icositetrachoral numbers.

1, 145, 1009, 3745, 10081, 22321, 43345, 76609, 126145, 196561, 293041, 421345, 587809, 799345, 1063441, 1388161, 1782145, 2254609, 2815345, 3474721, 4243681, 5133745, 6157009, 7326145, 8654401, 10155601, 11844145, 13735009, 15843745, 18186481

Offset

1,2

Comments

A icositetrachoral number is a centered figurate number that represents a icositetrachoron, which is a four-dimensional regular polytope composed of 24 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..30.

Eric Weisstein's World of Mathematics, Figurate Number.

Wikipedia, 24-cell.

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

Formula

a(n) = 24*n^4 - 48*n^3 + 48*n^2 - 24*n + 1.

G.f.: x*(1 + 140*x + 294*x^2 + 140*x^3 + x^4)/(1 - x)^5. - Stefano Spezia, Aug 26 2023

Mathematica

Table[24*n^4 - 48*n^3 + 48*n^2 - 24*n + 1, {n, 1, 100}]

Crossrefs

Cf. A362863, A365205, A365206.

Sequence in context: A297732 A354669 A296972 * A269015 A234116 A232151

Adjacent sequences: A365201 A365202 A365203 * A365205 A365206 A365207

Keyword

nonn,easy

Author

Léo Cymrot Cymbalista, Aug 25 2023

Status

approved