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%I A362863 #31 Aug 06 2023 17:48:46
%S A362863 1,1441,11521,44641,122401,273601,534241,947521,1563841,2440801,
%T A362863 3643201,5243041,7319521,9959041,13255201,17308801,22227841,28127521,
%U A362863 35130241,43365601,52970401,64088641,76871521,91477441,108072001,126828001,147925441,171551521,197900641
%N A362863 Centered hecatonicosachoral numbers.
%C A362863 A hecatonicosachoral number is a centered figurate number that represents a hecatonicosachoron, which is a four-dimensional regular polytope composed of 120 cells.
%C A362863 One of the 6 centered regular polichoral (centered pentachoral, centered hexadecachoral, centered octachoral, centered icositetrachoral, centered hexacosichoral and centered hecatonicosachoral) numbers.
%H A362863 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FigurateNumber.html">Figurate Number</a>.
%H A362863 Wikipedia, <a href="https://en.wikipedia.org/wiki/120-cell">120-cell</a>.
%H A362863 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A362863 a(n) = 300*n^4 - 600*n^3 + 420*n^2 - 120*n + 1.
%F A362863 a(n) = 1440*A006322(n-1) + 1 for n > 1.
%F A362863 a(n) = 288*(A151989(n-1)-1)/25 + 1.
%F A362863 G.f.: x*(1 + 1436*x + 4326*x^2 + 1436*x^3 + x^4)/(1 - x)^5. - _Stefano Spezia_, May 12 2023
%t A362863 Table[300*n^4 - 600*n^3 + 420*n^2 - 120*n + 1, {n, 1, 100}]
%Y A362863 Cf. A005891 (2D), A005904 (3D), A006322, A151989.
%K A362863 nonn,easy
%O A362863 1,2
%A A362863 _Léo Cymrot Cymbalista_, May 06 2023

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