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A362863 Centered hecatonicosachoral numbers. 3
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 (list; graph; refs; listen; history; text; internal format)
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
Eric Weisstein's World of Mathematics, Figurate Number.
Wikipedia, 120-cell.
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}]
CROSSREFS
Cf. A005891 (2D), A005904 (3D), A006322, A151989.
Sequence in context: A207200 A119422 A166609 * A178275 A220651 A252224
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified April 23 15:20 EDT 2024. Contains 371916 sequences. (Running on oeis4.)