A365206 Centered octachoral numbers.

1, 49, 337, 1249, 3361, 7441, 14449, 25537, 42049, 65521, 97681, 140449, 195937, 266449, 354481, 462721, 594049, 751537, 938449, 1158241, 1414561, 1711249, 2052337, 2442049, 2884801, 3385201, 3948049, 4578337, 5281249, 6062161, 6926641, 7880449, 8929537

Offset

1,2

Comments

A octachoral number is a centered figurate number that represents a octachoron, which is a four-dimensional regular polytope composed of 8 cells (also known as tesseract).

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..33.

Eric Weisstein's World of Mathematics, Figurate Number.

Wikipedia, 8-cell.

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

Formula

a(n) = 8*n^4 - 16*n^3 + 16*n^2 - 8n + 1.

G.f.: x*(1 + 44*x + 102*x^2 + 44*x^3 + x^4)/(1 - x)^5. - Stefano Spezia, Aug 26 2023

Mathematica

Table[8*n^4 - 16*n^3 + 16*n^2 - 8n + 1, {n, 1, 100}]

Crossrefs

Cf. A001844 (2D), A005917 (3D), A362863, A365204, A365205.

Sequence in context: A017474 A335389 A036318 * A020323 A036322 A036324

Adjacent sequences: A365203 A365204 A365205 * A365207 A365208 A365209

Keyword

nonn,easy

Author

Léo Cymrot Cymbalista, Aug 25 2023

Status

approved