The On-Line Encyclopedia of Integer Sequences (OEIS)

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A062154

Number T(n,m) of n X m matrices over {0,1,2} with all row and column sums equal to 1 or 2, m=0,..,2*n.
(history; published version)

#14 by Joerg Arndt at Sun Aug 18 02:01:02 EDT 2024

STATUS

reviewed

approved

#13 by Michel Marcus at Sun Aug 18 01:49:23 EDT 2024

STATUS

proposed

reviewed

#12 by Jason Yuen at Sat Aug 17 23:35:58 EDT 2024

STATUS

editing

proposed

#11 by Jason Yuen at Sat Aug 17 23:35:55 EDT 2024

EXAMPLE

T(2, 2)=13, i.e. there are 13 2 X 2 matrices over {0, 1, 2) } with all row and column sums equal to 1 or 2: [0 1 / 0 1], [0 1 / 0 2], [0 2 / 1 0], [1 0 / 1 0], [1 1 / 1 1], [1 1 / 2 0], [2 0 / 1 0], [1 1 / 2 0], [1 0 / 2 0], [0 1 / 0 2], [1 1 / 0 1], [1 0 / 1 1], [0 1 / 0 2].

STATUS

approved

editing

#10 by Alois P. Heinz at Wed Feb 03 20:08:56 EST 2021

STATUS

proposed

approved

#9 by Andrew Howroyd at Wed Feb 03 19:29:53 EST 2021

STATUS

editing

proposed

#8 by Andrew Howroyd at Wed Feb 03 19:28:58 EST 2021

KEYWORD

easy,nonn,tabf,easy,changed

#7 by Andrew Howroyd at Wed Feb 03 19:27:43 EST 2021

LINKS

Andrew Howroyd, <a href="/A062154/b062154.txt">Table of n, a(n) for n = 0..960</a> (rows 0..30)

CROSSREFS

Final terms of each row are A000680.

#6 by Andrew Howroyd at Wed Feb 03 19:21:12 EST 2021

LINKS

Andrew Howroyd, <a href="/A062154/b062154.txt">Table of n, a(n) for n = 0..960</a>

EXAMPLE

[1], [0, 2, 1], [0, 1, 13, 18, 6], [0, 0, 18, 189, 450, 360, 90], [0, 0, 6, 450, 4842, 16380, 22140, 12600, 2520], [0, 0, 0, 360, 16380, 190080, 832950, 1631700, 1537200, 680400, 113400], [0, 0, 0, 90, 22140, 832950, 10520010, 56609280, 147533400, 200377800, 144585000, 52390800, 7484400], ...

Triangle begins:

[0] 1;

[1] 0, 2, 1;

[2] 0, 1, 13, 18, 6;

[3] 0, 0, 18, 189, 450, 360, 90;

[4] 0, 0, 6, 450, 4842, 16380, 22140, 12600, 2520;

[5] 0, 0, 0, 360, 16380, 190080, 832950, 1631700, 1537200, 680400, 113400;

[6] 0, 0, 0, 90, 22140, 832950, 10520010, 56609280, 147533400, 200377800, 144585000, 52390800, 7484400;

PROG

(PARI)

Row(n)={Vecrev(serlaplace(n!*polcoef((1/sqrt(1-x*y + O(x*x^n))*exp(x*y/2+1/(1-x*y)*(x*y+x^2*y/2+x*y^2/2) + O(x*x^n))), n)))}

{ for(n=0, 6, print(Row(n))) } \\ Andrew Howroyd, Feb 03 2021

CROSSREFS

Row sums: are A062155, A062156.

Main diagonal is A062156.

STATUS

approved

editing

#5 by Charles R Greathouse IV at Fri May 10 12:44:47 EDT 2013

AUTHOR

_Vladeta Jovovic (vladeta(AT)eunet.rs), _, Jun 06 2001

Discussion

Fri May 10

12:44

OEIS Server: https://oeis.org/edit/global/1911