A365205 - OEIS

%I #9 Sep 25 2023 07:30:34

%S 1,21,121,421,1101,2401,4621,8121,13321,20701,30801,44221,61621,83721,

%T 111301,145201,186321,235621,294121,362901,443101,535921,642621,

%U 764521,903001,1059501,1235521,1432621,1652421,1896601,2166901,2465121,2793121,3152821

%N Centered pentachoral numbers.

%C A pentachoral number is a centered figurate number that represents a pentachoron, which is a four-dimensional regular polytope composed of 5 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/5-cell">5-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) = 5*n^4/2 - 5*n^3 + 15*n^2/2 - 5*n + 1.

%F G.f.: x*(1 + 16*x + 26*x^2 + 16*x^3 + x^4)/(1 - x)^5. - _Stefano Spezia_, Aug 26 2023

%t Table[5/2*n^4 - 5*n^3 + 15/2*n^2 - 5*n + 1, {n, 1, 100}]

%Y Cf. A005448 (2D), A005898 (3D), A362863, A365204, A365206.

%K nonn,easy

%O 1,2

%A _Léo Cymrot Cymbalista_, Aug 25 2023