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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
OFFSET
1,2
COMMENTS
Intersection of A074377 and A274757.
FORMULA
G.f.: 63*x^2*(15+194*x+15*x^2) / ((1-x)*(1-194*x+x^2)*(1+194*x+x^2)).
a(n) = a(n-1)+37634*a(n-2)-37634*a(n-3)-a(n-4)+a(n-5). - Wesley Ivan Hurt, Apr 24 2021
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)/((1-x)*(1-194*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
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jul 04 2016
STATUS
approved