|
%I #8 Sep 26 2023 10:59:02
%S 1,7957,1185037,10596309577,1578130224697,14111253811878301,
%T 2101618114050816901,18792154258821103289617,
%U 2798754265133491448134897,25025774916617575492416996517,3727140237435880812247465267837,33327174817289665775049786996211801
%N Pentagonal numbers (A000326) which are also centered hexagonal numbers (A003215).
%H Colin Barker, <a href="/A254138/b254138.txt">Table of n, a(n) for n = 1..327</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1331714,-1331714,-1,1).
%F a(n) = a(n-1)+1331714*a(n-2)-1331714*a(n-3)-a(n-4)+a(n-5).
%F G.f.: -x*(x^4+7956*x^3-154634*x^2+7956*x+1) / ((x-1)*(x^2-1154*x+1)*(x^2+1154*x+1)).
%e 7957 is in the sequence because it is the 73rd pentagonal number and the 52nd centered hexagonal number.
%t LinearRecurrence[{1,1331714,-1331714,-1,1},{1,7957,1185037,10596309577,1578130224697},20] (* _Harvey P. Dale_, Sep 26 2023 *)
%o (PARI) Vec(-x*(x^4+7956*x^3-154634*x^2+7956*x+1)/((x-1)*(x^2-1154*x+1)*(x^2+1154*x+1)) + O(x^100))
%Y Cf. A000326, A003215, A254136, A254137.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Jan 26 2015
|
