A274756 Values of n such that 2*n+1 and 6*n+1 are both triangular numbers.

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

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) / ((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

Adjacent sequences: A274753 A274754 A274755 * A274757 A274758 A274759

Keyword

nonn,easy

Author

Colin Barker, Jul 04 2016

Status

approved