A250656 -id:A250656 - cp's OEIS frontend

A250657 Number of (3+1)X(n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

39, 70, 109, 156, 211, 274, 345, 424, 511, 606, 709, 820, 939, 1066, 1201, 1344, 1495, 1654, 1821, 1996, 2179, 2370, 2569, 2776, 2991, 3214, 3445, 3684, 3931, 4186, 4449, 4720, 4999, 5286, 5581, 5884, 6195, 6514, 6841, 7176, 7519, 7870, 8229, 8596, 8971

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Row 3 of A250656

			Some solutions for n=4
..1..0..0..0..0....1..0..0..0..0....1..1..1..1..1....1..0..0..0..0
..0..0..0..0..0....0..0..0..0..0....1..1..1..1..1....0..0..0..0..0
..0..0..0..0..0....1..1..1..1..1....0..0..0..0..1....1..1..1..1..1
..0..1..1..1..1....0..1..1..1..1....0..0..0..0..1....1..1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 4*n^2 + 19*n + 16

A250653 Number of (n+1)X(5+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

49, 103, 211, 427, 859, 1723, 3451, 6907, 13819, 27643, 55291, 110587, 221179, 442363, 884731, 1769467, 3538939, 7077883, 14155771, 28311547, 56623099, 113246203, 226492411, 452984827, 905969659, 1811939323, 3623878651

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Column 5 of A250656.

Since one edge length of the array is fixed, and the constraint is a Markov-type correlation between fixed-width lengths of the other edge, the generating function is computable by the usual transfer matrix method and therefore a rational polynomial. That predicts that there is a linear recurrence. - R. J. Mathar, May 25 2018

			Some solutions for n=4
..1..1..1..0..0..0....1..1..1..1..1..1....1..1..1..1..1..1....1..1..1..1..0..0
..0..0..0..0..0..0....1..1..1..1..1..1....1..1..1..1..1..1....0..0..0..0..0..0
..1..1..1..1..1..1....0..0..0..0..0..0....0..0..0..0..0..0....1..1..1..1..1..1
..1..1..1..1..1..1....0..0..0..0..0..0....0..0..0..0..0..0....1..1..1..1..1..1
..0..0..0..0..1..1....1..1..1..1..1..1....0..0..0..0..1..1....0..0..0..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A304387.

Empirical: a(n) = 3*a(n-1) - 2*a(n-2); also a(n) = 2^(n-1)*25 + (5*2^(n-1)-1)*5 + 2^(n+1).

It appears that a(n) = 27*2^n-5, which would make this coincide with A304387. - N. J. A. Sloane, May 13 2018

A250652 Number of (n+1)X(n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

9, 34, 109, 316, 859, 2234, 5625, 13816, 33271, 78838, 184309, 425972, 974835, 2211826, 4980721, 11141104, 24772591, 54788078, 120586221, 264241132, 576716779, 1254096874, 2717908969, 5872025576, 12650020839, 27179089894

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Diagonal of A250656

			Some solutions for n=4
..0..0..0..0..0....1..1..0..0..0....1..1..1..1..0....1..0..0..0..0
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..0....0..1..1..1..1....0..0..0..0..0....1..1..1..1..1
..0..0..0..0..0....0..1..1..1..1....0..0..0..0..0....0..0..1..1..1
..0..0..1..1..1....0..1..1..1..1....0..1..1..1..1....0..0..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..69

A250654 Number of (n+1) X (6+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

64, 134, 274, 554, 1114, 2234, 4474, 8954, 17914, 35834, 71674, 143354, 286714, 573434, 1146874, 2293754, 4587514, 9175034, 18350074, 36700154, 73400314, 146800634, 293601274, 587202554, 1174405114, 2348810234, 4697620474

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

			Some solutions for n=4:
..0..0..0..0..0..0..0....1..1..1..1..1..1..0....1..1..1..1..1..1..1
..0..0..1..1..1..1..1....0..0..0..0..0..0..0....0..0..0..0..0..0..0
..0..0..1..1..1..1..1....1..1..1..1..1..1..1....1..1..1..1..1..1..1
..0..0..1..1..1..1..1....1..1..1..1..1..1..1....1..1..1..1..1..1..1
..0..0..1..1..1..1..1....0..1..1..1..1..1..1....0..0..0..1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 6 of A250656.

Empirical: a(n) = 3*a(n-1) - 2*a(n-2); also a(n) = 2^(n-1)*36 + (5*2^(n-1)-1)*6 + 2^(n+1).

Empirical g.f.: 2*x*(32 - 29*x) / ((1 - x)*(1 - 2*x)). - Colin Barker, Nov 15 2018

A250655 Number of (n+1) X (7+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

81, 169, 345, 697, 1401, 2809, 5625, 11257, 22521, 45049, 90105, 180217, 360441, 720889, 1441785, 2883577, 5767161, 11534329, 23068665, 46137337, 92274681, 184549369, 369098745, 738197497, 1476395001, 2952790009, 5905580025

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

			Some solutions for n=4:
..1..1..0..0..0..0..0..0....1..1..1..1..0..0..0..0....1..1..1..1..0..0..0..0
..0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0
..0..0..0..0..1..1..1..1....0..0..0..1..1..1..1..1....1..1..1..1..1..1..1..1
..0..0..0..0..1..1..1..1....0..0..0..1..1..1..1..1....1..1..1..1..1..1..1..1
..0..0..0..0..1..1..1..1....0..0..0..1..1..1..1..1....0..0..0..0..0..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 7 of A250656.

Empirical: a(n) = 3*a(n-1) - 2*a(n-2); also a(n) = 2^(n-1)*49 + (5*2^(n-1)-1)*7 +2^(n+1).

Empirical g.f.: x*(81 - 74*x) / ((1 - x)*(1 - 2*x)). - Colin Barker, Nov 15 2018

A250658 Number of (4+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

79, 142, 221, 316, 427, 554, 697, 856, 1031, 1222, 1429, 1652, 1891, 2146, 2417, 2704, 3007, 3326, 3661, 4012, 4379, 4762, 5161, 5576, 6007, 6454, 6917, 7396, 7891, 8402, 8929, 9472, 10031, 10606, 11197, 11804, 12427, 13066, 13721, 14392, 15079, 15782

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

			Some solutions for n=4:
..1..1..1..1..1....0..0..0..0..0....1..1..1..0..0....1..1..1..0..0
..1..1..1..1..1....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..1....0..0..0..0..0
..1..1..1..1..1....0..0..0..0..0....0..0..0..0..1....0..1..1..1..1
..0..1..1..1..1....0..0..0..0..0....0..0..0..0..1....0..1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 4 of A250656.

Empirical: a(n) = 8*n^2 + 39*n + 32.
Conjectures from Colin Barker, Nov 15 2018: (Start)
G.f.: x*(79 - 95*x + 32*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)

A250659 Number of (5+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

159, 286, 445, 636, 859, 1114, 1401, 1720, 2071, 2454, 2869, 3316, 3795, 4306, 4849, 5424, 6031, 6670, 7341, 8044, 8779, 9546, 10345, 11176, 12039, 12934, 13861, 14820, 15811, 16834, 17889, 18976, 20095, 21246, 22429, 23644, 24891, 26170, 27481, 28824

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

			Some solutions for n=4:
..0..0..0..0..0....1..1..1..1..1....0..0..0..0..0....1..1..1..0..0
..1..1..1..1..1....1..1..1..1..1....1..1..1..1..1....0..0..0..0..0
..1..1..1..1..1....0..0..0..0..0....1..1..1..1..1....1..1..1..1..1
..0..0..0..0..0....1..1..1..1..1....1..1..1..1..1....1..1..1..1..1
..0..1..1..1..1....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..1..1..1..1....1..1..1..1..1....0..0..0..0..1....0..1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 5 of A250656.

Empirical: a(n) = 16*n^2 + 79*n + 64.
Conjectures from Colin Barker, Nov 15 2018: (Start)
G.f.: x*(159 - 191*x + 64*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)

A250660 Number of (6+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

319, 574, 893, 1276, 1723, 2234, 2809, 3448, 4151, 4918, 5749, 6644, 7603, 8626, 9713, 10864, 12079, 13358, 14701, 16108, 17579, 19114, 20713, 22376, 24103, 25894, 27749, 29668, 31651, 33698, 35809, 37984, 40223, 42526, 44893, 47324, 49819, 52378, 55001

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

			Some solutions for n=4:
..1..1..1..1..1....1..1..1..1..1....0..0..0..0..0....1..1..0..0..0
..1..1..1..1..1....0..0..0..0..0....1..1..1..1..1....0..0..0..0..0
..0..0..0..0..0....0..0..0..0..0....1..1..1..1..1....1..1..1..1..1
..0..0..0..0..0....0..0..0..0..0....1..1..1..1..1....0..0..0..0..0
..1..1..1..1..1....0..0..0..0..0....1..1..1..1..1....0..0..0..0..0
..0..0..0..0..1....1..1..1..1..1....1..1..1..1..1....1..1..1..1..1
..0..0..0..0..1....0..1..1..1..1....1..1..1..1..1....0..0..0..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 6 of A250656.

Empirical: a(n) = 32*n^2 + 159*n + 128.
Conjectures from Colin Barker, Nov 15 2018: (Start)
G.f.: x*(319 - 383*x + 128*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)

A250661 Number of (7+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Original entry on oeis.org

639, 1150, 1789, 2556, 3451, 4474, 5625, 6904, 8311, 9846, 11509, 13300, 15219, 17266, 19441, 21744, 24175, 26734, 29421, 32236, 35179, 38250, 41449, 44776, 48231, 51814, 55525, 59364, 63331, 67426, 71649, 76000, 80479, 85086, 89821, 94684, 99675

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

			Some solutions for n=4:
..1..1..1..1..1....1..1..0..0..0....1..1..0..0..0....0..0..0..0..0
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..0....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0
..1..1..1..1..1....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..1..1..1..1..1....0..0..0..0..0....0..0..0..0..0....1..1..1..1..1
..1..1..1..1..1....1..1..1..1..1....1..1..1..1..1....0..0..0..0..1
..0..0..0..0..0....1..1..1..1..1....0..0..0..0..0....0..0..0..0..1
..0..0..0..0..0....0..0..1..1..1....1..1..1..1..1....0..0..0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 7 of A250656.

Empirical: a(n) = 64*n^2 + 319*n + 256.
Conjectures from Colin Barker, Nov 16 2018: (Start)
G.f.: x*(639 - 767*x + 256*x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
(End)

A303273 Array T(n,k) = binomial(n, 2) + k*n + 1 read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 1, 3, 4, 4, 1, 4, 6, 7, 7, 1, 5, 8, 10, 11, 11, 1, 6, 10, 13, 15, 16, 16, 1, 7, 12, 16, 19, 21, 22, 22, 1, 8, 14, 19, 23, 26, 28, 29, 29, 1, 9, 16, 22, 27, 31, 34, 36, 37, 37, 1, 10, 18, 25, 31, 36, 40, 43, 45, 46, 46, 1, 11, 20, 28, 35, 41

Offset: 0

Franck Maminirina Ramaharo, Apr 20 2018

Columns are linear recurrence sequences with signature (3,-3,1).
8*T(n,k) + A166147(k-1) are squares.
Columns k are binomial transforms of [1, k, 1, 0, 0, 0, ...].
Antidiagonals sums yield A116731.

			The array T(n,k) begins
1    1    1    1    1    1    1    1    1    1    1    1    1  ...  A000012
1    2    3    4    5    6    7    8    9   10   11   12   13  ...  A000027
2    4    6    8   10   12   14   16   18   20   22   24   26  ...  A005843
4    7   10   13   16   19   22   25   28   31   34   37   40  ...  A016777
7   11   15   19   23   27   31   35   39   43   47   51   55  ...  A004767
11  16   21   26   31   36   41   46   51   56   61   66   71  ...  A016861
16  22   28   34   40   46   52   58   64   70   76   82   88  ...  A016957
22  29   36   43   50   57   64   71   78   85   92   99  106  ...  A016993
29  37   45   53   61   69   77   85   93  101  109  117  125  ...  A004770
37  46   55   64   73   82   91  100  109  118  127  136  145  ...  A017173
46  56   66   76   86   96  106  116  126  136  146  156  166  ...  A017341
56  67   78   89  100  111  122  133  144  155  166  177  188  ...  A017401
67  79   91  103  115  127  139  151  163  175  187  199  211  ...  A017605
79  92  105  118  131  144  157  170  183  196  209  222  235  ...  A190991
...
The inverse binomial transforms of the columns are
1    1    1    1    1    1    1    1    1    1    1    1    1  ...
0    1    2    3    4    5    6    7    8    9   10   11   12  ...
1    1    1    1    1    1    1    1    1    1    1    1    1  ...
0    0    0    0    0    0    0    0    0    0    0    0    0  ...
0    0    0    0    0    0    0    0    0    0    0    0    0  ...
0    0    0    0    0    0    0    0    0    0    0    0    0  ...
...
T(k,n-k) = A087401(n,k) + 1 as triangle
1
1   1
1   2   2
1   3   4   4
1   4   6   7   7
1   5   8  10  11  11
1   6  10  13  15  16  16
1   7  12  16  19  21  22  22
1   8  14  19  23  26  28  29  29
1   9  16  22  27  31  34  36  37  37
1  10  18  25  31  36  40  43  45  46  46
...

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics: A Foundation for Computer Science, Addison-Wesley, 1994.

Cf. A085475, A086270, A086271, A086272, A086273, A130154, A159798, A162609, A162610, A300401.

T := (n, k) -> binomial(n, 2) + k*n + 1;
for n from 0 to 20 do seq(T(n, k), k = 0 .. 20) od;

Table[With[{n = m - k}, Binomial[n, 2] + k n + 1], {m, 0, 11}, {k, m, 0, -1}] // Flatten (* Michael De Vlieger, Apr 21 2018 *)

T(n, k) := binomial(n, 2)+ k*n + 1$
for n:0 thru 20 do
    print(makelist(T(n, k), k, 0, 20));

T(n,k) = binomial(n, 2) + k*n + 1;
tabl(nn) = for (n=0, nn, for (k=0, nn, print1(T(n, k), ", ")); print); \\ Michel Marcus, May 17 2018

G.f.: (3*x^2*y - 3*x*y + y - 2*x^2 + 2*x - 1)/((x - 1)^3*(y - 1)^2).
E.g.f.: (1/2)*(2*x*y + x^2 + 2)*exp(y + x).
T(n,k) = 3*T(n-1,k) - 3*T(n-2,k) + T(n-3,k), with T(0,k) = 1, T(1,k) = k + 1 and T(2,k) = 2*k + 2.
T(n,k) = T(n-1,k) + n + k - 1.
T(n,k) = T(n,k-1) + n, with T(n,0) = 1.
T(n,0) = A152947(n+1).
T(n,1) = A000124(n).
T(n,2) = A000217(n).
T(n,3) = A034856(n+1).
T(n,4) = A052905(n).
T(n,5) = A051936(n+4).
T(n,6) = A246172(n+1).
T(n,7) = A302537(n).
T(n,8) = A056121(n+1) + 1.
T(n,9) = A056126(n+1) + 1.
T(n,10) = A051942(n+10) + 1, n > 0.
T(n,11) = A101859(n) + 1.
T(n,12) = A132754(n+1) + 1.
T(n,13) = A132755(n+1) + 1.
T(n,14) = A132756(n+1) + 1.
T(n,15) = A132757(n+1) + 1.
T(n,16) = A132758(n+1) + 1.
T(n,17) = A212427(n+1) + 1.
T(n,18) = A212428(n+1) + 1.
T(n,n) = A143689(n) = A300192(n,2).
T(n,n+1) = A104249(n).
T(n,n+2) = T(n+1,n) = A005448(n+1).
T(n,n+3) = A000326(n+1).
T(n,n+4) = A095794(n+1).
T(n,n+5) = A133694(n+1).
T(n+2,n) = A005449(n+1).
T(n+3,n) = A115067(n+2).
T(n+4,n) = A133694(n+2).
T(2*n,n) = A054556(n+1).
T(2*n,n+1) = A054567(n+1).
T(2*n,n+2) = A033951(n).
T(2*n,n+3) = A001107(n+1).
T(2*n,n+4) = A186353(4*n+1) (conjectured).
T(2*n,n+5) = A184103(8*n+1) (conjectured).
T(2*n,n+6) = A250657(n-1) = A250656(3,n-1), n > 1.
T(n,2*n) = A140066(n+1).
T(n+1,2*n) = A005891(n).
T(n+2,2*n) = A249013(5*n+4) (conjectured).
T(n+3,2*n) = A186384(5*n+3) = A186386(5*n+3) (conjectured).
T(2*n,2*n) = A143689(2*n).
T(2*n+1,2*n+1) = A143689(2*n+1) (= A030503(3*n+3) (conjectured)).
T(2*n,2*n+1) = A104249(2*n) = A093918(2*n+2) = A131355(4*n+1) (= A030503(3*n+5) (conjectured)).
T(2*n+1,2*n) = A085473(n).
a(n+1,5*n+1)=A051865(n+1) + 1.
a(n,2*n+1) = A116668(n).
a(2*n+1,n) = A054569(n+1).
T(3*n,n) = A025742(3*n-1), n > 1 (conjectured).
T(n,3*n) = A140063(n+1).
T(n+1,3*n) = A069099(n+1).
T(n,4*n) = A276819(n).
T(4*n,n) = A154106(n-1), n > 0.
T(2^n,2) = A028401(n+2).
T(1,n)*T(n,1) = A006000(n).
T(n*(n+1),n) = A211905(n+1), n > 0 (conjectured).
T(n*(n+1)+1,n) = A294259(n+1).
T(n,n^2+1) = A081423(n).
T(n,A000217(n)) = A158842(n), n > 0.
T(n,A152947(n+1)) = A060354(n+1).
floor(T(n,n/2)) = A267682(n) (conjectured).
floor(T(n,n/3)) = A025742(n-1), n > 0 (conjectured).
floor(T(n,n/4)) = A263807(n-1), n > 0 (conjectured).
ceiling(T(n,2^n)/n) = A134522(n), n > 0 (conjectured).
ceiling(T(n,n/2+n)/n) = A051755(n+1) (conjectured).
floor(T(n,n)/n) = A133223(n), n > 0 (conjectured).
ceiling(T(n,n)/n) = A007494(n), n > 0.
ceiling(T(n,n^2)/n) = A171769(n), n > 0.
ceiling(T(2*n,n^2)/n) = A046092(n), n > 0.
ceiling(T(2*n,2^n)/n) = A131520(n+2), n > 0.

cp's OEIS Frontend

A250657 Number of (3+1)X(n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Views

Author

Keywords

Comments

Examples

Links

Formula

A250653 Number of (n+1)X(5+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A250652 Number of (n+1)X(n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Views

Author

Keywords

Comments

Examples

Links

A250654 Number of (n+1) X (6+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A250655 Number of (n+1) X (7+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A250658 Number of (4+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A250659 Number of (5+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A250660 Number of (6+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A250661 Number of (7+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A303273 Array T(n,k) = binomial(n, 2) + k*n + 1 read by antidiagonals.

Views

Author

Keywords

Comments

Examples

References