A223637 -id:A223637 - cp's OEIS frontend

A223632 Number of n X 3 0..1 arrays with rows, antidiagonals and columns unimodal.

7, 49, 229, 801, 2297, 5699, 12657, 25753, 48811, 87253, 148501, 242425, 381837, 583031, 866369, 1256913, 1785103, 2487481, 3407461, 4596145, 6113185, 8027691, 10419185, 13378601, 17009331, 21428317, 26767189, 33173449, 40811701, 49864927

Offset: 1

R. H. Hardin, Mar 24 2013

nonn

Column 3 of A223637.

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

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

Cf. A223637.

Empirical: a(n) = (23/360)*n^6 + (11/120)*n^5 + (91/72)*n^4 + (11/8)*n^3 + (301/180)*n^2 + (23/15)*n + 1.
Conjectures from Colin Barker, Aug 21 2018: (Start)
G.f.: x*(7 + 33*x^2 - 18*x^3 + 29*x^4 - 6*x^5 + x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A223633 Number of n X 4 0..1 arrays with rows, antidiagonals and columns unimodal.

Original entry on oeis.org

11, 121, 801, 3712, 13599, 42109, 114713, 282273, 639165, 1350228, 2689169, 5091414, 9224755, 16081503, 27096217, 44293439, 70470225, 109418622, 166193601, 247432316, 361730919, 520085521, 736404249, 1028097709, 1416755525

Offset: 1

R. H. Hardin, Mar 24 2013

nonn

Column 4 of A223637.

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

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

Cf. A223637.

Empirical: a(n) = (1/112)*n^8 - (1/72)*n^7 + (203/360)*n^6 + (37/360)*n^5 + (41/144)*n^4 + (901/36)*n^3 - (168481/2520)*n^2 + (5693/60)*n - 45 for n>2.
Conjectures from Colin Barker, Aug 21 2018: (Start)
G.f.: x*(11 + 22*x + 108*x^2 - 65*x^3 + 249*x^4 - 74*x^5 + 92*x^6 + 18*x^7 + 9*x^8 - 11*x^9 + x^10) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>11.
(End)

A223634 Number of nX5 0..1 arrays with rows, antidiagonals and columns unimodal.

Original entry on oeis.org

16, 256, 2297, 13599, 61545, 230619, 748950, 2171533, 5738616, 14032520, 32116856, 69421945, 142742110, 280837253, 531285626, 970419825, 1717396652, 2953706474, 4949721932, 8100222189, 12971210226, 20360769871, 31377189150, 47538110053

Offset: 1

R. H. Hardin Mar 24 2013

nonn

Column 5 of A223637

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

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

A223635 Number of nX6 0..1 arrays with rows, antidiagonals and columns unimodal.

Original entry on oeis.org

22, 484, 5699, 42109, 230619, 1026377, 3907140, 13135511, 39889555, 111242770, 288488044, 702553878, 1619299148, 3555008655, 7473337157, 15110365462, 29495673113, 55765989646, 102405932407, 183099750019, 319441371676

Offset: 1

R. H. Hardin Mar 24 2013

nonn

Column 6 of A223637

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

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

Empirical: a(n) = (271/5443200)*n^12 - (10327/9979200)*n^11 + (61997/2177280)*n^10 - (21923/80640)*n^9 + (417761/1814400)*n^8 + (37222841/604800)*n^7 - (2521405483/2177280)*n^6 + (8668581613/725760)*n^5 - (414044081579/5443200)*n^4 + (88564150211/302400)*n^3 - (17419930607/30240)*n^2 + (542846047/3080)*n + 850576 for n>8

A223636 Number of nX7 0..1 arrays with rows, antidiagonals and columns unimodal.

Original entry on oeis.org

29, 841, 12657, 114713, 748950, 3907140, 17224974, 66448428, 229624238, 723456027, 2106393383, 5727793388, 14669871333, 35633091730, 82556882471, 183320486518, 391738700030, 808400385799, 1615892668057, 3136875572418

Offset: 1

R. H. Hardin Mar 24 2013

nonn

Column 7 of A223637

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

R. H. Hardin, Table of n, a(n) for n = 1..201

Empirical: a(n) = (503/209563200)*n^14 - (76217/778377600)*n^13 + (88483/23950080)*n^12 - (1160261/17107200)*n^11 + (158917/435456)*n^10 + (88785757/3628800)*n^9 - (2720678887/3048192)*n^8 + (182706654569/10886400)*n^7 - (2182833462133/10886400)*n^6 + (2369225181061/1555200)*n^5 - (18729229340021/2993760)*n^4 + (2512793025389/9979200)*n^3 + (795324348531341/5821200)*n^2 - (56828168983661/90090)*n + 981755694 for n>12

A223631 Number of n X n 0..1 arrays with rows, antidiagonals and columns unimodal.

Original entry on oeis.org

2, 16, 229, 3712, 61545, 1026377, 17224974, 291563806, 4984273228, 86086143903, 1502219415538

Offset: 1

R. H. Hardin Mar 24 2013

nonn

Diagonal of A223637

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

cp's OEIS Frontend

A223632 Number of n X 3 0..1 arrays with rows, antidiagonals and columns unimodal.

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A223633 Number of n X 4 0..1 arrays with rows, antidiagonals and columns unimodal.

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A223634 Number of nX5 0..1 arrays with rows, antidiagonals and columns unimodal.

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A223635 Number of nX6 0..1 arrays with rows, antidiagonals and columns unimodal.

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A223636 Number of nX7 0..1 arrays with rows, antidiagonals and columns unimodal.

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A223631 Number of n X n 0..1 arrays with rows, antidiagonals and columns unimodal.

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