A254137 - OEIS

%I #8 Jun 13 2015 00:55:22

%S 1,52,629,59432,725289,68583900,836982301,79145760592,965876849489,

%T 91334139138692,1114621047327429,105399517420289400,

%U 1286271722739003001,121630951768874828332,1484356453419762135149,140362012941764131605152,1712946060974682764958369

%N Indices of centered hexagonal numbers (A003215) which are also pentagonal numbers (A000326).

%C Also positive integers y in the solutions to 3*x^2 - 6*y^2 - x + 6*y - 2 = 0, the corresponding values of x being A254136.

%H Colin Barker, <a href="/A254137/b254137.txt">Table of n, a(n) for n = 1..653</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1154,-1154,-1,1).

%F a(n) = a(n-1)+1154*a(n-2)-1154*a(n-3)-a(n-4)+a(n-5).

%F G.f.: x*(51*x^3+577*x^2-51*x-1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).

%e 52 is in the sequence because the 52nd centered hexagonal number is 7957, which is also the 73rd pentagonal number.

%o (PARI) Vec(x*(51*x^3+577*x^2-51*x-1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))

%Y Cf. A000326, A003215, A254136, A254138.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 26 2015