

A274756


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


3



0, 945, 13167, 35578242, 495540990, 1338951572595, 18649189618605, 50390103447476100, 701843601611053692, 1896381151803363988917, 26413182084381205040235, 71368408216577696911440390, 994033693861758668873164410, 2685878672926303893761783662455
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OFFSET

1,2


COMMENTS

Intersection of A074377 and A274757.


LINKS

Colin Barker, Table of n, a(n) for n = 1..400
Index entries for linear recurrences with constant coefficients, signature (1,37634,37634,1,1).


FORMULA

G.f.: 63*x^2*(15+194*x+15*x^2) / ((1x)*(1194*x+x^2)*(1+194*x+x^2)).


EXAMPLE

945 is in the sequence because 2*945+1 = 1891, 6*945+1 = 5671, and 1891 and 5671 are both triangular numbers.


PROG

(PARI) isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(6*n+1, 3)
(PARI) concat(0, Vec(63*x^2*(15+194*x+15*x^2)/((1x)*(1194*x+x^2)*(1+194*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), A274680 (2*n+1 and 4*n+1).
Sequence in context: A293186 A294027 A127666 * A335053 A290034 A335055
Adjacent sequences: A274753 A274754 A274755 * A274757 A274758 A274759


KEYWORD

nonn,easy


AUTHOR

Colin Barker, Jul 04 2016


STATUS

approved



