A131235 -id:A131235 - cp's OEIS frontend

A131236 Row sums of A131235.

1, 2, 5, 14, 48, 190, 873, 4504, 25989, 164686, 1141079, 8550794, 69034238, 596165874, 5489044279, 53611773888, 553937164945, 6032197300602, 69070616521369, 829210595494742, 10416695090023412, 136614200179164806, 1867352453003735541

Offset: 0

Vladeta Jovovic, Jun 20 2007

A131236 := proc(d)
    add( A131235(d-m,m),m=0..d) ;
end proc:
seq(A131236(n),n=0..20) ; # R. J. Mathar, Mar 20 2018

Extended by R. J. Mathar, Mar 20 2018

A049088 Number of n X n matrices with nonnegative integer entries and every row and column sum <= 2.

Original entry on oeis.org

1, 3, 26, 451, 12951, 551681, 32512618, 2525962461, 249675308081, 30551602194811, 4528860725614746, 799069823975939363, 165374947602000265231, 39654053930039468491521, 10900817711883556591556906, 3404265715022353551494548021, 1198175785461867097633422235713

Offset: 0

N. J. A. Sloane, Jan 23 2000

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.65(b).

Cf. A073178, A073179. Diagonal of A131235.

Stanley gives an explicit generating function.

A131237 Number of n X (n+1) matrices with nonnegative integer entries and every row and column sum <= 2.

Original entry on oeis.org

1, 6, 79, 1837, 66021, 3374176, 231848191, 20570267229, 2285620096717, 310524073877026, 50598503336716611, 9732804817777566361, 2180831456691952213969, 562835395375423511668692, 165687992856606963112408291, 55166524646338775672718351481, 20620925283916296038124156761241

Offset: 0

Vladeta Jovovic, Jun 20 2007

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.65(a).

Cf. A049088, A131235, A131236.

A131237 := proc(n)
        exp((x*y*(3-x*y)/2+(x+y)*(2-x*y)/2)/(1-x*y))/sqrt(1-x*y) ;
        coeftayl(%,y=0,n+1) ;
        coeftayl(%,x=0,n) ;
        %*(n+1)!*n! ;
        simplify(%) ;
end proc: # R. J. Mathar, Sep 30 2011

A301390 The number of n X k matrices, k=0..n, with nonnegative integer entries and every row and column sum <=3 . Triangle T(n>=0, 0<=k<=n) read by rows.

Original entry on oeis.org

1, 1, 4, 1, 10, 70, 1, 20, 316, 3380, 1, 35, 1045, 23259, 344279, 1, 56, 2806, 112976, 3286101, 63241196, 1, 84, 6510, 427440, 21787375, 789333776, 18937075894, 1, 120, 13560, 1347676, 109770025, 6797996276, 296755137820, 8610006123300, 1, 165, 26001, 3702285, 449707069, 43808767121, 3202666462485, 164411906603281, 5637949058244465

Offset: 0

R. J. Mathar, Mar 20 2018

			1
1  4
1 10   70
1 20  316   3380
1 35 1045  23259   344279
1 56 2806 112976  3286101  63241196
1 84 6510 427440 21787375 789333776 18937075894

Alois P. Heinz, Rows n = 0..10, flattened

Cf. A131235 (sums <= 2), A086885 (sums <= 1), A000292 (row-column 1).

T(n,k) = T(k,n). T(n,0)=1 (the empty matrix).

G.f. column k=2 polynomial is -(1+x)*(6*x^4-18*x^3+19*x^2+2*x+1)/(x-1)^7.

More terms from Alois P. Heinz, Mar 20 2018

cp's OEIS Frontend

A131236 Row sums of A131235.

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A049088 Number of n X n matrices with nonnegative integer entries and every row and column sum <= 2.

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A131237 Number of n X (n+1) matrices with nonnegative integer entries and every row and column sum <= 2.

Views

Author

Keywords

References

Crossrefs

Programs

Maple

A301390 The number of n X k matrices, k=0..n, with nonnegative integer entries and every row and column sum <=3 . Triangle T(n>=0, 0<=k<=n) read by rows.

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