A251863 - OEIS

%I #8 Jun 13 2015 00:55:19

%S 2,147,3102,170407,3580474,196650299,4131864662,226934275407,

%T 4768168240242,261881957170147,5502462017375374,302211551640074999,

%U 6349836399882942122,348751868710689379467,7327705703002897834182,402459354280583903830687

%N Numbers n such that the sum of the octagonal numbers N(n), N(n+1) and N(n+2) is equal to the sum of the pentagonal numbers P(m), P(m+1), P(m+2) for some m.

%C Also nonnegative integers x in the solutions to 18*x^2-9*y^2+24*x-15*y+6 = 0, the corresponding values of y being A251864.

%H Colin Barker, <a href="/A251863/b251863.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*(x^4+25*x^3-647*x^2-145*x-2) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).

%e 2 is in the sequence because N(2)+N(3)+N(4) = 8+21+40 = 69 = 12+22+35 = P(3)+P(4)+P(5).

%o (PARI) Vec(x*(x^4+25*x^3-647*x^2-145*x-2)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))

%Y Cf. A000326, A000567, A251864.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Dec 10 2014