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
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
KEYWORD
nonn,easy
AUTHOR
Léo Cymrot Cymbalista, Aug 25 2023
STATUS
approved