A054731 Numbers of the form x*(x + 1)*y*(y + 1)/4 where x and y are distinct.

0, 3, 6, 10, 15, 18, 21, 28, 30, 36, 45, 55, 60, 63, 66, 78, 84, 90, 91, 105, 108, 120, 126, 135, 136, 150, 153, 165, 168, 171, 190, 198, 210, 216, 231, 234, 253, 270, 273, 276, 280, 300, 315, 325, 330, 351, 360, 378, 396, 406, 408, 420, 435, 450, 459, 465, 468

Offset: 1

Author

Stuart M. Ellerstein (ellerstein(AT)aol.com), Apr 22 2000

Keywords

• nonn
• easy

Crossrefs

Cf. A053990, A054734. Contains all triangular numbers >1.

Programs

Mathematica

With[{upto=500},Select[Union[(#[[1]](#[[1]]+1)#[[2]](#[[2]]+1))/4&/@ Subsets[ Range[0,Floor[upto/2]],{2}]],#<=upto&]] (* Harvey P. Dale, Jan 15 2015 *)

Formula

a(n) = A053990(n) / 4. - Sean A. Irvine, Feb 19 2022

Extensions

More terms from James Sellers, Apr 22 2000