cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Léo Cymrot Cymbalista

Léo Cymrot Cymbalista's wiki page.

Léo Cymrot Cymbalista has authored 4 sequences.

A365206 Centered octachoral numbers.

Original entry on oeis.org

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

Views

Author

Léo Cymrot Cymbalista, Aug 25 2023

Keywords

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

Crossrefs

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

Programs

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

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

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

Views

Author

Léo Cymrot Cymbalista, Aug 25 2023

Keywords

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

Crossrefs

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

Programs

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

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

A365204 Centered icositetrachoral numbers.

Original entry on oeis.org

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

Views

Author

Léo Cymrot Cymbalista, Aug 25 2023

Keywords

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

Crossrefs

Cf. A362863, A365205, A365206.

Programs

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

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

A362863 Centered hecatonicosachoral numbers.

Original entry on oeis.org

1, 1441, 11521, 44641, 122401, 273601, 534241, 947521, 1563841, 2440801, 3643201, 5243041, 7319521, 9959041, 13255201, 17308801, 22227841, 28127521, 35130241, 43365601, 52970401, 64088641, 76871521, 91477441, 108072001, 126828001, 147925441, 171551521, 197900641
Offset: 1

Views

Author

Léo Cymrot Cymbalista, May 06 2023

Keywords

Comments

A hecatonicosachoral number is a centered figurate number that represents a hecatonicosachoron, which is a four-dimensional regular polytope composed of 120 cells.
One of the 6 centered regular polichoral (centered pentachoral, centered hexadecachoral, centered octachoral, centered icositetrachoral, centered hexacosichoral and centered hecatonicosachoral) numbers.

Links

Crossrefs

Cf. A005891 (2D), A005904 (3D), A006322, A151989.

Programs

  • Mathematica
    Table[300*n^4 - 600*n^3 + 420*n^2 - 120*n + 1, {n, 1, 100}]

Formula

a(n) = 300*n^4 - 600*n^3 + 420*n^2 - 120*n + 1.
a(n) = 1440*A006322(n-1) + 1 for n > 1.
a(n) = 288*(A151989(n-1)-1)/25 + 1.
G.f.: x*(1 + 1436*x + 4326*x^2 + 1436*x^3 + x^4)/(1 - x)^5. - Stefano Spezia, May 12 2023

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