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A274680
Values of n such that 2*n+1 and 4*n+1 are both triangular numbers.
5
0, 16065, 545751, 21394547226, 726784809030, 28491418065071115, 967869505172593485, 37942420317086720855700, 1288925370210688376036076, 50528452330120333959563160501, 1716479960463788790499334882595, 67289447366315927998308608003134830
OFFSET
1,2
FORMULA
Intersection of A074377 and A274681.
G.f.: 459*x^2*(35+1154*x+35*x^2) / ((1-x)*(1-1154*x+x^2)*(1+1154*x+x^2)).
EXAMPLE
16065 is in the sequence because 2*16065+1 = 32131, 4*16065+1 = 64261, and 32131 and 64261 are both triangular numbers.
MATHEMATICA
Rest@ CoefficientList[Series[459 x^2 (35 + 1154 x + 35 x^2)/((1 - x) (1 - 1154 x + x^2) (1 + 1154 x + x^2)), {x, 0, 12}], x] (* Michael De Vlieger, Jul 02 2016 *)
PROG
(PARI) isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(4*n+1, 3)
(PARI) concat(0, Vec(459*x^2*(35+1154*x+35*x^2)/((1-x)*(1-1154*x+x^2)*(1+1154*x+x^2)) + O(x^20)))
CROSSREFS
Cf. A124174 (2*n+1 and 9*n+1), A274579 (2*n+1 and 5*n+1), A274603 (2*n+1 and 3*n+1).
Sequence in context: A202420 A031839 A062674 * A286662 A222419 A252603
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jul 02 2016
STATUS
approved