A252985 - OEIS

%I #7 Jun 13 2015 00:55:20

%S 1,579,1870,835278,2696899,1204470657,3888926848,1736845852476,

%T 5607829818277,2504530514800095,8086486709028946,3611531265495884874,

%U 11660708226589922215,5207825580314551188573,16814733176255958805444,7509680875282317318037752

%N Numbers n such that the sum of the hexagonal numbers X(n) and X(n+1) is equal to the heptagonal number H(m) for some m.

%C Also positive integers x in the solutions to 8*x^2-5*y^2+4*x+3*y+2 = 0, the corresponding values of y being A252986.

%H Colin Barker, <a href="/A252985/b252985.txt">Table of n, a(n) for n = 1..633</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1442,-1442,-1,1).

%F a(n) = a(n-1)+1442*a(n-2)-1442*a(n-3)-a(n-4)+a(n-5).

%F G.f.: x*(68*x^3+151*x^2-578*x-1) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)).

%e 1 is in the sequence because X(1)+X(2) = 1+6 = 7 = H(2).

%o (PARI) Vec(x*(68*x^3+151*x^2-578*x-1)/((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100))

%Y Cf. A000384, A000566, A252986.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Dec 25 2014