A254895 - OEIS

%I #6 Jun 13 2015 00:55:25

%S 1,13,53,1241,5161,121573,505693,11912881,49552721,1167340733,

%T 4855660933,114387478921,475805218681,11208805593493,46624055769773,

%U 1098348560683361,4568681660219041,107626950141375853,447684178645696213,10546342765294150201

%N Indices of octagonal numbers (A000567) that are also centered square numbers (A001844).

%C Also positive integers x in the solutions to 6*x^2 - 4*y^2 - 4*x + 4*y - 2 = 0, the corresponding values of y being A253673.

%H Colin Barker, <a href="/A254895/b254895.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,98,-98,-1,1).

%F a(n) = a(n-1)+98*a(n-2)-98*a(n-3)-a(n-4)+a(n-5).

%F G.f.: -x*(x^4+12*x^3-58*x^2+12*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).

%e 13 is in the sequence because the 13th octagonal number is 481, which is also the 16th centered square number.

%o (PARI) Vec(-x*(x^4+12*x^3-58*x^2+12*x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))

%Y Cf. A000567, A001844, A253673, A254896.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Feb 10 2015