A251793 - OEIS

%I #7 Jun 13 2015 00:55:19

%S 0,2,68,286,6760,28122,662508,2755766,64919120,270037042,6361411348,

%T 26460874446,623353393080,2592895658762,61082271110588,

%U 254077313684326,5985439215444640,24896983845405282,586511960842464228,2439650339536033406

%N Numbers n such that the sum of the triangular numbers T(n) and T(n+1) is equal to the sum of the octagonal numbers N(m) and N(m+1) for some m.

%C Also nonnegative integers y in the solutions to 6*x^2-y^2+2*x-2*y = 0, the corresponding values of x being A220755.

%H Colin Barker, <a href="/A251793/b251793.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.: -2*x^2*(3*x^3+11*x^2+33*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).

%e 68 is in the sequence because T(68)+T(69) = 2346+2415 = 4761 = 2296+2465 = N(28)+N(29).

%o (PARI) concat(0, Vec(-2*x^2*(3*x^3+11*x^2+33*x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100)))

%Y Cf. A000217, A000567, A220755.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Dec 09 2014