A362863 - OEIS

%I #31 Aug 06 2023 17:48:46

%S 1,1441,11521,44641,122401,273601,534241,947521,1563841,2440801,

%T 3643201,5243041,7319521,9959041,13255201,17308801,22227841,28127521,

%U 35130241,43365601,52970401,64088641,76871521,91477441,108072001,126828001,147925441,171551521,197900641

%N Centered hecatonicosachoral numbers.

%C A hecatonicosachoral number is a centered figurate number that represents a hecatonicosachoron, which is a four-dimensional regular polytope composed of 120 cells.

%C One of the 6 centered regular polichoral (centered pentachoral, centered hexadecachoral, centered octachoral, centered icositetrachoral, centered hexacosichoral and centered hecatonicosachoral) numbers.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FigurateNumber.html">Figurate Number</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/120-cell">120-cell</a>.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n) = 300*n^4 - 600*n^3 + 420*n^2 - 120*n + 1.

%F a(n) = 1440*A006322(n-1) + 1 for n > 1.

%F a(n) = 288*(A151989(n-1)-1)/25 + 1.

%F G.f.: x*(1 + 1436*x + 4326*x^2 + 1436*x^3 + x^4)/(1 - x)^5. - _Stefano Spezia_, May 12 2023

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

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

%K nonn,easy

%O 1,2

%A _Léo Cymrot Cymbalista_, May 06 2023