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%I #7 Jun 13 2015 00:55:20
%S 1,871,2841,1006671,3280049,1161698999,3785175241,1340599639711,
%T 4368088949601,1547050822529031,5040770862665849,1785295308598863599,
%U 5817045207427441681,2060229239072266065751,6712865128600405035561,2377502756594086441014591
%N Numbers n such that the sum of the pentagonal numbers P(n), P(n+1), P(n+2) and P(n+3) is equal to the octagonal number O(m) for some m.
%C Also positive integers x in the solutions to 12*x^2-6*y^2+32*x+4*y+36 = 0, the corresponding values of y being A253168.
%H Colin Barker, <a href="/A253167/b253167.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+150*x^3-816*x^2-870*x-1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).
%e 1 is in the sequence because P(1)+P(2)+P(3)+P(4) = 1+5+12+22 = 40 = O(4).
%o (PARI) Vec(x*(x^4+150*x^3-816*x^2-870*x-1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))
%Y Cf. A000326, A000567, A253168.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Dec 29 2014
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