A223644 -id:A223644 - cp's OEIS frontend

A223639 Number of n X 3 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

7, 49, 218, 726, 2014, 4904, 10797, 21917, 41601, 74635, 127636, 209480, 331776, 509386, 760991, 1109703, 1583723, 2217045, 3050206, 4131082, 5515730, 7269276, 9466849, 12194561, 15550533, 19645967, 24606264, 30572188, 37701076, 46168094

Offset: 1

R. H. Hardin, Mar 24 2013

nonn

Column 3 of A223644.

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

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

Cf. A223644.

Empirical: a(n) = (23/360)*n^6 - (3/40)*n^5 + (31/18)*n^4 + (5/8)*n^3 + (1517/360)*n^2 - (51/20)*n + 3.
Conjectures from Colin Barker, Aug 22 2018: (Start)
G.f.: x*(7 + 22*x^2 - 16*x^3 + 40*x^4 - 10*x^5 + 3*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)

A223640 Number of n X 4 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

Original entry on oeis.org

11, 121, 726, 2962, 9808, 28450, 74599, 179991, 404599, 855417, 1714062, 3275798, 6002946, 10596004, 18086161, 29953249, 48273537, 75902131, 116695104, 175776840, 259858436, 377613366, 540116971, 761356699, 1058820379, 1454170173

Offset: 1

R. H. Hardin, Mar 24 2013

nonn

Column 4 of A223644.

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

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

Cf. A223644.

Empirical: a(n) = (1/112)*n^8 - (19/210)*n^7 + (107/90)*n^6 - (197/40)*n^5 + (2219/144)*n^4 + (5093/120)*n^3 - (868411/2520)*n^2 + (417721/420)*n - 1091 for n>4.
Conjectures from Colin Barker, Aug 22 2018: (Start)
G.f.: x*(11 + 22*x + 33*x^2 - 140*x^3 + 508*x^4 - 314*x^5 - 17*x^6 + 432*x^7 - 233*x^8 + 28*x^9 + 56*x^10 - 28*x^11 + 2*x^12) / (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>13.
(End)

A223641 Number of nX5 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

Original entry on oeis.org

16, 256, 2014, 9808, 36947, 120307, 354726, 967582, 2469396, 5941152, 13555296, 29475566, 61346859, 122671803, 236477826, 440811016, 796753648, 1399853788, 2396080742, 4003682172, 6542620323, 10473608867, 16449161244, 25379498938

Offset: 1

R. H. Hardin Mar 24 2013

nonn

Column 5 of A223644

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

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

Empirical: a(n) = (359/453600)*n^10 - (391/18144)*n^9 + (27901/60480)*n^8 - (5318/945)*n^7 + (220373/5400)*n^6 + (42079/4320)*n^5 - (611182913/181440)*n^4 + (204761033/5670)*n^3 - (1618325179/8400)*n^2 + (680702213/1260)*n - 629380 for n>7

A223642 Number of nX6 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

Original entry on oeis.org

22, 484, 4904, 28450, 120307, 428187, 1370104, 4063584, 11337648, 29980136, 75501066, 181755554, 419574383, 931417149, 1993443114, 4122964868, 8258744026, 16054980456, 30348305906, 55882034882, 100405014805, 176305599685

Offset: 1

R. H. Hardin Mar 24 2013

nonn

Column 6 of A223644

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

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

Empirical: a(n) = (271/5443200)*n^12 - (5527/1995840)*n^11 + (55709/544320)*n^10 - (179285/72576)*n^9 + (69131681/1814400)*n^8 - (2290717/10080)*n^7 - (649163341/136080)*n^6 + (54977562187/362880)*n^5 - (2886586169891/1360800)*n^4 + (1624780719439/90720)*n^3 - (17508153293/189)*n^2 + (926735309999/3465)*n - 321893740 for n>13

A223643 Number of nX7 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

Original entry on oeis.org

29, 841, 10797, 74599, 354726, 1370104, 4682514, 14767708, 43862845, 124004457, 335617558, 872372014, 2182675327, 5267049151, 12280118231, 27708360959, 60600014150, 128659653568, 265553503693, 533599565121, 1045268782162

Offset: 1

R. H. Hardin Mar 24 2013

nonn

Column 7 of A223644

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

R. H. Hardin, Table of n, a(n) for n = 1..78

Empirical: a(n) = (503/209563200)*n^14 - (185069/778377600)*n^13 + (1733819/119750400)*n^12 - (7176551/11975040)*n^11 + (36644381/2177280)*n^10 - (480531353/1814400)*n^9 - (76780811581/76204800)*n^8 + (29262582467/155520)*n^7 - (62420351374933/10886400)*n^6 + (281872655928541/2721600)*n^5 - (74234681724454753/59875200)*n^4 + (3261809312979967/332640)*n^3 - (557318597695013723/11642400)*n^2 + (14542780178794541/120120)*n - 90173668357 for n>19

A223638 Number of n X n 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

Original entry on oeis.org

2, 16, 218, 2962, 36947, 428187, 4682514, 49045356, 497721760, 4944054774

Offset: 1

R. H. Hardin Mar 24 2013

nonn

Diagonal of A223644

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

cp's OEIS Frontend

A223639 Number of n X 3 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A223640 Number of n X 4 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A223641 Number of nX5 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

Views

Author

Keywords

Comments

Examples

Links

Formula

A223642 Number of nX6 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

Views

Author

Keywords

Comments

Examples

Links

Formula

A223643 Number of nX7 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

Views

Author

Keywords

Comments

Examples

Links

Formula

A223638 Number of n X n 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

Views

Author

Keywords

Comments

Examples