A365204 - OEIS

%I #10 Sep 25 2023 07:30:09

%S 1,145,1009,3745,10081,22321,43345,76609,126145,196561,293041,421345,

%T 587809,799345,1063441,1388161,1782145,2254609,2815345,3474721,

%U 4243681,5133745,6157009,7326145,8654401,10155601,11844145,13735009,15843745,18186481

%N Centered icositetrachoral numbers.

%C A icositetrachoral number is a centered figurate number that represents a icositetrachoron, which is a four-dimensional regular polytope composed of 24 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/24-cell">24-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) = 24*n^4 - 48*n^3 + 48*n^2 - 24*n + 1.

%F G.f.: x*(1 + 140*x + 294*x^2 + 140*x^3 + x^4)/(1 - x)^5. - _Stefano Spezia_, Aug 26 2023

%t Table[24*n^4 - 48*n^3 + 48*n^2 - 24*n + 1, {n, 1, 100}]

%Y Cf. A362863, A365205, A365206.

%K nonn,easy

%O 1,2

%A _Léo Cymrot Cymbalista_, Aug 25 2023