A365206 -id:A365206 - cp's OEIS frontend

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

Léo Cymrot Cymbalista, Aug 25 2023

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.

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).

Cf. A362863, A365205, A365206.

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

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

A365205 Centered pentachoral numbers.

Original entry on oeis.org

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

Léo Cymrot Cymbalista, Aug 25 2023

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

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).

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

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

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

cp's OEIS Frontend

A365204 Centered icositetrachoral numbers.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula