A279042 Numbers k such that 2*k+1 and 10*k+1 are both triangular numbers (A000217).
4455, 30537, 461938302, 3166172226, 47894687058501, 328275068740587, 4965816943137597372, 34036215673995404100, 514865832250497683700195, 3528942913182916419190605, 53382319214430283898266055610, 365887859090594924500524938502
Offset: 1
Examples
4455 is in the sequence because 2*4455+1 = 8911 and 10*4455+1 = 44551 are both triangular numbers.
Links
- Colin Barker, Table of n, a(n) for n = 1..350
- Index entries for linear recurrences with constant coefficients, signature (1,103682,-103682,-1,1).
Programs
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Mathematica
LinearRecurrence[{1, 103682, -103682, -1, 1}, {4455, 30537, 461938302, 3166172226, 47894687058501}, 20] (* Vincenzo Librandi, Dec 05 2016 *) -
PARI
Vec(81*x*(55 + 322*x + 55*x^2) / ((1 - x)*(1 - 322*x + x^2)*(1 + 322*x + x^2)) + O(x^15))
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PARI
isok(k) = ispolygonal(2*k+1, 3) & ispolygonal(10*k+1, 3)
Formula
a(n) = a(n-1) + 103682*a(n-2) - 103682*a(n-3) - a(n-4) + a(n-5) for n>5.
G.f.: 81*x*(55 + 322*x + 55*x^2) / ((1 - x)*(1 - 322*x + x^2)*(1 + 322*x + x^2)).