A053990 -id:A053990 - cp's OEIS frontend

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

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

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

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

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

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

Cf. A085780 (one quarter of this).

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

More terms from James Sellers, Jul 23 2002

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

Original entry on oeis.org

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

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

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

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 *)

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

More terms from James Sellers, Apr 22 2000

A054734 Numbers of the form 2x(x + 1)y(y + 1) where x and y are distinct.

Original entry on oeis.org

0, 24, 48, 80, 120, 144, 168, 224, 240, 288, 360, 440, 480, 504, 528, 624, 672, 720, 728, 840, 864, 960, 1008, 1080, 1088, 1200, 1224, 1320, 1344, 1368, 1520, 1584, 1680, 1728, 1848, 1872, 2024, 2160, 2184, 2208, 2240, 2400, 2520, 2600, 2640, 2808

Offset: 1

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

Cf. A053990, A054731.

a(n) = 2 * A053990(n). - Sean A. Irvine, Feb 20 2022

More terms from James Sellers, Apr 22 2000

A049207 Array T(m,n) of products of pronic numbers m(m+1) * n(n+1) read by antidiagonals ("bipronics").

Original entry on oeis.org

0, 0, 0, 0, 4, 0, 0, 12, 12, 0, 0, 24, 36, 24, 0, 0, 40, 72, 72, 40, 0, 0, 60, 120, 144, 120, 60, 0, 0, 84, 180, 240, 240, 180, 84, 0, 0, 112, 252, 360, 400, 360, 252, 112, 0, 0, 144, 336, 504, 600, 600, 504, 336, 144, 0, 0, 180, 432, 672, 840, 900, 840, 672, 432, 180, 0, 0

Offset: 0

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

			Array begins
0 0 0 0 0 0 ...
0 4 12 24 40 ...
0 12 36 72 120 ...
0 24 72 144 240 ...

Cf. A002378, A072389, A053990.

T := (m,n)->m*(m+1)*n*(n+1): seq(seq(T(q-p,p),p=0..q),q=0..12);

Corrected and extended by Emeric Deutsch, Mar 04 2004

cp's OEIS Frontend

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

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

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A054734 Numbers of the form 2x(x + 1)y(y + 1) where x and y are distinct.

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Author

Keywords

Crossrefs

Formula

Extensions

A049207 Array T(m,n) of products of pronic numbers m(m+1) * n(n+1) read by antidiagonals ("bipronics").

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

Extensions

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Extensions

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

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula

Extensions

A054734 Numbers of the form 2*x*(x + 1)*y*(y + 1) where x and y are distinct.

Views

Author

Keywords

Crossrefs

Formula

Extensions

A049207 Array T(m,n) of products of pronic numbers m(m+1) * n(n+1) read by antidiagonals ("bipronics").

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

Extensions

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

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

A054734 Numbers of the form 2x(x + 1)y(y + 1) where x and y are distinct.