A362863 - OEIS

A362863

Centered hecatonicosachoral numbers.

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

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OFFSET

1,2

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

Table of n, a(n) for n=1..29.

Eric Weisstein's World of Mathematics, Figurate Number.

Wikipedia, 120-cell.

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

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

MATHEMATICA

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