A072389 Numbers of the form x*(x+1) * y*(y+1) ("bipronics") with x and y nonnegative integers.

0, 4, 12, 24, 36, 40, 60, 72, 84, 112, 120, 144, 180, 220, 240, 252, 264, 312, 336, 360, 364, 400, 420, 432, 480, 504, 540, 544, 600, 612, 660, 672, 684, 760, 792, 840, 864, 900, 924, 936, 1012, 1080, 1092, 1104, 1120, 1200, 1260, 1300, 1320

Offset

1,2

Comments

Nonnegative numbers k = a*b = c*d, where a+b = c+d+1. - Yifan Xie, Jun 28 2024

Links

John Drake, Table of n, a(n) for n = 1..10000

Example

a(3) = 1*2*2*3 = 12.

Prog

(PARI) A003056(n)=(sqrtint(8*n+1)-1)\2
list(lim)=my(v=List([0]), t); for(a=1, A003056(lim\4), t=a*(a+1); for(b=a, A003056(lim\t\2), listput(v, b*(b+1)*t))); Set(v) \\ Charles R Greathouse IV, Jul 11 2024

Crossrefs

Cf. A053990 (sequence of bipronics with x and y distinct).

Cf. A085780 (one quarter of this).

Sequence in context: A008077 A301265 A285350 * A218391 A297568 A353795

Adjacent sequences: A072386 A072387 A072388 * A072390 A072391 A072392

Keyword

nonn,easy

Author

Stuart M. Ellerstein (ellerstein(AT)aol.com), Jul 20 2002

Extensions

More terms from James Sellers, Jul 23 2002

Status

approved