A250797 -id:A250797 - cp's OEIS frontend

A250791 Number of (n+1) X (2+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

24, 66, 180, 490, 1336, 3646, 9956, 27194, 74288, 202950, 554460, 1514802, 4138504, 11306590, 30890164, 84393482, 230567264, 629921462, 1720977420, 4701797730, 12845550264, 35094695950, 95880492388, 261950376634, 715661738000

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

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

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

Column 2 of A250797.

Empirical: a(n) = 4*a(n-1) - 3*a(n-2) - 2*a(n-3) + 2*a(n-4).
Conjectures from Colin Barker, Nov 20 2018: (Start)
G.f.: 2*x*(12 - 15*x - 6*x^2 + 8*x^3) / ((1 - x)^2*(1 - 2*x - 2*x^2)).
a(n) = (-6 + (39-23*sqrt(3))*(1-sqrt(3))^n + 39*(1+sqrt(3))^n + 23*sqrt(3)*(1+sqrt(3))^n + 6*n) / 9.
(End)

A250792 Number of (n+1) X (3+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

54, 162, 482, 1430, 4258, 12706, 37986, 113694, 340562, 1020650, 3059890, 9175558, 27518466, 82538994, 247584194, 742687022, 2227929970, 6683527738, 20050058898, 60149128086, 180445287074, 541331666882, 1623986612002, 4871943058750

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

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

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

Column 3 of A250797.

Empirical: a(n) = 6*a(n-1) - 10*a(n-2) + 11*a(n-4) - 6*a(n-5).
Conjectures from Colin Barker, Nov 20 2018: (Start)
G.f.: 2*x*(27 - 81*x + 25*x^2 + 79*x^3 - 48*x^4) / ((1 - x)^2*(1 + x)*(1 - 2*x)*(1 - 3*x)).
a(n) = -3 - (-1)^n/4 + 2^(1+n) + (23*3^(1+n))/4 + n.
(End)

A250793 Number of (n+1) X (4+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

118, 376, 1190, 3776, 12062, 38676, 124366, 400616, 1292134, 4171276, 13474406, 43546448, 140781326, 455247108, 1472416318, 4762930232, 15408574198, 49852141564, 161298304598, 521908159904, 1688775756830, 5464620624372

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

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

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

Column 4 of A250797.

Empirical: a(n) = 8*a(n-1) - 20*a(n-2) + 8*a(n-3) + 33*a(n-4) - 36*a(n-5) + 8*a(n-7).

Empirical g.f.: 2*x*(59 - 284*x + 271*x^2 + 416*x^3 - 624*x^4 + 10*x^5 + 128*x^6) / ((1 - x)^2*(1 - 2*x)*(1 - 2*x - x^2)*(1 - 2*x - 4*x^2)). - Colin Barker, Nov 20 2018

A250794 Number of (n+1) X (5+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

252, 838, 2776, 9258, 31220, 105954, 361344, 1236058, 4237556, 14549610, 50012080, 172050098, 592248148, 2039649282, 7026884288, 24215293674, 83465955764, 287740551770, 992085339216, 3420905014178, 11796889975188, 40683768017330

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

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

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

Column 5 of A250797.

Empirical: a(n) = 10*a(n-1) - 33*a(n-2) + 24*a(n-3) + 79*a(n-4) - 138*a(n-5) - 3*a(n-6) + 100*a(n-7) - 18*a(n-8) - 20*a(n-9).

Empirical g.f.: 2*x*(126 - 841*x + 1356*x^2 + 1552*x^3 - 4886*x^4 + 609*x^5 + 3484*x^6 - 580*x^7 - 640*x^8) / ((1 - x)^2*(1 - 2*x)*(1 - 2*x - x^2)*(1 - 2*x - 2*x^2)*(1 - 2*x - 5*x^2)). - Colin Barker, Nov 20 2018

A250795 Number of (n+1) X (6+1) 0..1 arrays with nondecreasing min(x(i,j), x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

530, 1818, 6230, 21610, 76110, 270598, 968942, 3485538, 12580830, 45517150, 164970110, 598685226, 2174802030, 7906183238, 28758522030, 104655742642, 380990823486, 1387358367918, 5053131325982, 18408177907066, 67069331582158

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

Column 6 of A250797.

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

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

Cf. A250797.

Empirical: a(n) = 12*a(n-1) -49*a(n-2) +50*a(n-3) +165*a(n-4) -408*a(n-5) +a(n-6) +618*a(n-7) -224*a(n-8) -344*a(n-9) +108*a(n-10) +72*a(n-11).

A250796 Number of (n+1)X(7+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

1102, 3868, 13598, 48600, 177142, 653880, 2437366, 9144752, 34478398, 130446176, 494830430, 1880740552, 7158985446, 27281746344, 104059447110, 397187462784, 1516879760334, 5795614884304, 22151486206382, 84689884626136

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

Column 7 of A250797

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

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

Empirical: a(n) = 14*a(n-1) -68*a(n-2) +88*a(n-3) +312*a(n-4) -1008*a(n-5) +62*a(n-6) +2576*a(n-7) -1535*a(n-8) -2790*a(n-9) +1886*a(n-10) +1456*a(n-11) -656*a(n-12) -336*a(n-13)

A250798 Number of (1+1) X (n+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

10, 24, 54, 118, 252, 530, 1102, 2272, 4654, 9486, 19260, 38986, 78726, 158672, 319318, 641830, 1288828, 2586018, 5185566, 10393024, 20821470, 41700254, 83493244, 167136538, 334515862, 669424560, 1339484742, 2679997942, 5361659964

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

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

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

Row 1 of A250797.

Empirical: a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3).

Empirical g.f.: 2*x*(5 - 3*x - 4*x^2) / ((1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 20 2018

A250799 Number of (2+1) X (n+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

24, 66, 162, 376, 838, 1818, 3868, 8114, 16842, 34680, 70974, 144562, 293356, 593562, 1198210, 2414360, 4857750, 9762474, 19600956, 39324898, 78848794, 158019576, 316560142, 633963266, 1269290508, 2540787978, 5085146898, 10176071704

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

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

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

Row 2 of A250797.

Empirical: a(n) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).

Empirical g.f.: 2*x*(12 - 15*x - 3*x^2 + 8*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 20 2018

A250800 Number of (3+1) X (n+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

58, 180, 482, 1190, 2776, 6230, 13598, 29084, 61274, 127630, 263544, 540558, 1102982, 2241420, 4540290, 9173622, 18497880, 37239590, 74873806, 150386236, 301805898, 605284030, 1213273912, 2430926110, 4868936566, 9749335980

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

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

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

Row 3 of A250797.

Empirical: a(n) = 5*a(n-1) - 8*a(n-2) + 3*a(n-3) + 3*a(n-4) - 2*a(n-5).

Empirical g.f.: 2*x*(29 - 55*x + 23*x^2 + 23*x^3 - 16*x^4) / ((1 - x)^2*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 20 2018

A250801 Number of (4+1) X (n+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

Original entry on oeis.org

140, 490, 1430, 3776, 9258, 21610, 48600, 106426, 228342, 482496, 1007546, 2084962, 4284032, 8754018, 17810278, 36111264, 73018218, 147325946, 296740456, 596862762, 1199199990, 2407260800, 4828861690, 9680929586, 19399411088

Offset: 1

R. H. Hardin, Nov 27 2014

nonn

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

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

Row 4 of A250797.

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 9*a(n-3) + 9*a(n-4) + 6*a(n-5) - 8*a(n-6) -a(n-7) + 2*a(n-8).

Empirical g.f.: 2*x*(70 - 35*x - 125*x^2 + 148*x^3 + 82*x^4 - 125*x^5 - 15*x^6 + 32*x^7) / ((1 - x)^3*(1 + x)^2*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Nov 20 2018

cp's OEIS Frontend

A250791 Number of (n+1) X (2+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

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A250792 Number of (n+1) X (3+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

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A250793 Number of (n+1) X (4+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

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A250794 Number of (n+1) X (5+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

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A250795 Number of (n+1) X (6+1) 0..1 arrays with nondecreasing min(x(i,j), x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

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A250796 Number of (n+1)X(7+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

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A250798 Number of (1+1) X (n+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

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A250799 Number of (2+1) X (n+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

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A250800 Number of (3+1) X (n+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

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A250801 Number of (4+1) X (n+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

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