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Centered triangular numbers (A005448) which are also centered octagonal numbers (A016754).
3

%I #8 Dec 09 2017 14:42:32

%S 1,361,6241,3463321,59923081,33254804881,575381414521,319312633001041,

%T 5524812282304561,3066039868821187801,53049246959306977201,

%U 29440114501108412261161,509378863778453312776441,282683976373603105710477121,4891055796951461749972406281

%N Centered triangular numbers (A005448) which are also centered octagonal numbers (A016754).

%H Colin Barker, <a href="/A253675/b253675.txt">Table of n, a(n) for n = 1..503</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,9602,-9602,-1,1).

%F a(n) = a(n-1)+9602*a(n-2)-9602*a(n-3)-a(n-4)+a(n-5).

%F G.f.: -x*(x^4+360*x^3-3722*x^2+360*x+1) / ((x-1)*(x^2-98*x+1)*(x^2+98*x+1)).

%e 361 is in the sequence because it is the 16th centered triangular number and the 10th centered octagonal number.

%t LinearRecurrence[{1,9602,-9602,-1,1},{1,361,6241,3463321,59923081},20] (* _Harvey P. Dale_, Dec 09 2017 *)

%o (PARI) Vec(-x*(x^4+360*x^3-3722*x^2+360*x+1)/((x-1)*(x^2-98*x+1)*(x^2+98*x+1)) + O(x^100))

%Y Cf. A005448, A016754, A253673, A253674.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 08 2015