A253579 - OEIS

%I #9 Jun 13 2015 00:55:21

%S 1,22801,1666681,47411143081,3465632747641,98584929298781641,

%T 7206305041398228481,204993755756525779060081,

%U 14984516863488437537571601,426256225957302372068628976801,31158234954289838149958560780201,886340998518823181233611960679431001

%N Centered pentagonal numbers (A005891) which are also centered octagonal numbers (A016754).

%H Colin Barker, <a href="/A253579/b253579.txt">Table of n, a(n) for n = 1..317</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2079362,-2079362,-1,1).

%F a(n) = a(n-1)+2079362*a(n-2)-2079362*a(n-3)-a(n-4)+a(n-5).

%F G.f.: -x*(x^4+22800*x^3-435482*x^2+22800*x+1) / ((x-1)*(x^2-1442*x+1)*(x^2+1442*x+1)).

%e 22801 is in the sequence because it is the 96th centered pentagonal number and the 76th centered octagonal number.

%o (PARI) Vec(-x*(x^4+22800*x^3-435482*x^2+22800*x+1)/((x-1)*(x^2-1442*x+1)*(x^2+1442*x+1)) + O(x^100))

%Y Cf. A005891, A016754, A253410, A253411.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 04 2015