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 A274579 Values of n such that 2*n+1 and 5*n+1 are both triangular numbers. 6

%I

%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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Last modified January 26 01:48 EST 2020. Contains 331270 sequences. (Running on oeis4.)