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%I #16 Jul 08 2016 11:13:43
%S 0,1,7,27,540,2002,10660,39501,779247,2887450,15372280,56960982,
%T 1123674201,4163701465,22166817667,82137697110,1620337419162,
%U 6004054625647,31964535704101,118442502272205,2336525434757970,8657842606482076,46092838318496542
%N Values of n such that 2*n+1 and 5*n+1 are both triangular numbers.
%C Intersection of A074377 and A085787.
%H Colin Barker, <a href="/A274579/b274579.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1442,-1442,0,0,-1,1).
%F G.f.: x^2*(1+6*x+20*x^2+513*x^3+20*x^4+6*x^5+x^6) / ((1-x)*(1+6*x-x^2)*(1-6*x-x^2)*(1+38*x^2+x^4)).
%e 7 is in the sequence because 2*7+1 = 15, 5*7+1 = 36, and 15 and 36 are both triangular numbers.
%o (PARI) concat(0, Vec(x^2*(1+6*x+20*x^2+513*x^3+20*x^4+6*x^5+x^6)/((1-x)*(1+6*x-x^2)*(1-6*x-x^2)*(1+38*x^2+x^4)) + O(x^30)))
%o (PARI) isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(5*n+1, 3); \\ _Michel Marcus_, Jun 29 2016
%Y Cf. A074377, A085787, A124174.
%K nonn,easy
%O 1,3
%A _Colin Barker_, Jun 29 2016
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