A250676 -id:A250676 - cp's OEIS frontend

A250544 T(n,k) = number of (n+1)X(k+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction.

150, 1080, 1080, 6627, 10704, 6627, 36552, 79366, 79366, 36552, 187000, 491650, 644779, 491650, 187000, 905440, 2701872, 4169584, 4169584, 2701872, 905440, 4206453, 13657024, 23289547, 27240292, 23289547, 13657024, 4206453, 18933408

Offset: 1

R. H. Hardin, Nov 24 2014

Peter Luschny remarks that the coefficients of the empirical recurrence relation for the column 1 are listed in the 9th row of A246117. - M. F. Hasler, Feb 11 2015

			Some solutions for n=2 k=4
..2..2..1..0..0....2..0..3..1..1....2..2..2..2..0....0..0..2..0..0
..2..3..2..2..2....0..0..3..2..2....2..2..2..2..0....1..1..3..1..1
..1..3..2..3..3....0..0..3..2..3....1..2..2..2..3....0..0..2..0..2
Table starts:
.......150.......1080........6627........36552........187000........905440
......1080......10704.......79366.......491650.......2701872......13657024
......6627......79366......644779......4169584......23289547.....117777788
.....36552.....491650.....4169584.....27240292.....151170400.....752602024
....187000....2701872....23289547....151170400.....824599694....4013192386
....905440...13657024...117777788....752602024....4013192386...19031828420
...4206453...64993652...555362165...3475227442...18064444143...83356429646
..18933408..295871112..2489782728..15210145612...76961701472..345394150196
..83153850.1302924116.10756619019..64036997144..315204675572.1375930596944
.358250280.5595784456.45218540866.262068107390.1254564769204.5328628464360

R. H. Hardin, Table of n, a(n) for n = 1..144

Row/column 1 is A223069(n+1) and row/column 2 of A223071.
Row/column 2-7 are A250538 - A250543; diagonal is A250537.
See also A250676, A250669 - A250675, A250691, A250692...

Empirical for column k (k=2-7 recurrence also works for k=1):
k=1: a(n) = 16*a(n-1) -106*a(n-2) +376*a(n-3) -769*a(n-4) +904*a(n-5) -564*a(n-6) +144*a(n-7)
k=2: [order 16, see A250538]
k=3: [same order 16]
k=4: [same order 16]
k=5: [same order 16]
k=6: [same order 16]
k=7: [same order 16]

Edited by M. F. Hasler, Feb 11 2015

A250669 Number of (n+1)X(1+1) 0..3 arrays with nondecreasing 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

104, 520, 2512, 11736, 53032, 233300, 1005121, 4260728, 17835379, 73930174, 304111433, 1243471948, 5060483311, 20518170938, 82950532885, 334582615528, 1347111707003, 5416107760342, 21751360774177, 87278063198468

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Column 1 of A250676

			Some solutions for n=4
..2..1....2..0....0..2....2..0....0..0....0..0....1..1....1..0....2..1....0..1
..0..3....1..2....1..1....1..1....0..2....0..1....0..2....0..1....0..3....0..3
..2..1....1..2....1..1....0..2....1..1....1..3....1..3....0..1....0..3....0..3
..3..0....2..1....2..2....0..2....2..2....2..2....2..2....0..3....3..0....2..1
..0..3....2..2....1..3....1..1....3..1....2..3....2..2....2..1....0..3....1..3

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

Empirical: a(n) = 16*a(n-1) -106*a(n-2) +376*a(n-3) -769*a(n-4) +904*a(n-5) -564*a(n-6) +144*a(n-7) for n>11

A250675 Number of (n+1)X(7+1) 0..3 arrays with nondecreasing 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

3321772, 115965426, 2996016017, 61498698426, 1070591197687, 15971487229178, 210335029800118, 2486539928867930, 26773801460595558, 265593229627937954, 2450139707701747024, 21184357574916340526, 172798870644903483178

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Column 7 of A250676

			Some solutions for n=1
..0..0..1..1..2..3..2..0....0..0..1..0..2..1..1..1....0..0..2..1..1..0..0..0
..0..0..1..1..2..3..2..1....0..0..1..0..2..1..1..2....0..0..3..0..2..1..1..3

R. H. Hardin, Table of n, a(n) for n = 1..27

A250677 Number of (1+1) X (n+1) 0..3 arrays with nondecreasing 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

104, 669, 3927, 22119, 120233, 637948, 3321772, 17052553, 86573591, 435717423, 2177845221, 10825761528, 53576004128, 264200974309, 1299108852679, 6372932446759, 31203614429489, 152543921033076, 744788303718996

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Row 1 of A250676.

			Some solutions for n=4:
  2 1 3 1 1    1 2 1 0 1    1 2 2 0 0    1 1 1 1 3
  3 2 2 3 3    1 3 2 1 2    2 3 1 1 1    1 2 3 3 1

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

Cf. A250676.

Empirical: a(n) = 10*a(n-1) - 21*a(n-2) - 54*a(n-3) + 155*a(n-4) + 118*a(n-5) - 228*a(n-6) - 144*a(n-7).

Empirical g.f.: x*(104 - 371*x - 579*x^2 + 2514*x^3 + 1516*x^4 - 3792*x^5 - 2304*x^6) / ((1 - 4*x)*(1 - x - x^2)*(1 - 2*x - 4*x^2)*(1 - 3*x - 9*x^2)). - Colin Barker, Mar 19 2018

A250683 Number of (7+1)X(n+1) 0..3 arrays with nondecreasing 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

1005121, 32230991, 923242475, 23739860017, 542694735983, 11161659240791, 210335029800118, 3682042848693451, 60641209583699449, 948745856029597670, 14215547255379464689, 205309451238359552540, 2873492420605039758875

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Row 7 of A250676

			Some solutions for n=1
..0..2....0..1....0..0....0..0....0..1....0..0....0..0....0..1....0..1....0..0
..0..2....0..3....0..0....0..2....0..3....0..3....0..2....0..2....0..1....0..2
..2..0....2..1....0..2....2..0....2..1....0..3....0..3....2..0....0..3....2..0
..2..1....3..0....0..3....2..2....0..3....3..0....1..2....0..2....2..1....0..2
..0..3....1..2....3..0....3..1....1..2....3..1....1..2....2..0....2..2....2..0
..2..1....0..3....1..3....1..3....3..0....1..3....2..1....2..0....3..1....0..3
..3..0....1..2....3..1....3..1....2..1....2..2....1..2....3..1....2..3....2..1
..2..3....2..3....3..1....2..2....3..0....1..3....2..3....3..1....3..2....3..0

R. H. Hardin, Table of n, a(n) for n = 1..17

A250670 Number of (n+1)X(2+1) 0..3 arrays with nondecreasing 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

669, 5154, 34630, 210158, 1185860, 6325144, 32230991, 158164928, 752162284, 3484008326, 15783790118, 70176461116, 307081524576, 1325658002144, 5657123014959, 23904700805062, 100166248075189, 416720321036830

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Column 2 of A250676

			Some solutions for n=3
..1..0..2....2..1..1....0..0..2....2..0..1....3..0..1....3..1..1....1..0..2
..1..0..3....2..1..1....0..1..1....1..1..2....3..0..2....3..1..1....0..1..1
..2..2..1....2..1..3....0..1..2....1..1..2....3..2..0....3..2..0....0..2..2
..3..1..3....2..1..3....1..3..0....1..1..3....2..3..1....3..2..3....1..1..3

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

Empirical: a(n) = 38*a(n-1) -678*a(n-2) +7552*a(n-3) -58895*a(n-4) +341814*a(n-5) -1531840*a(n-6) +5427992*a(n-7) -15445215*a(n-8) +35639986*a(n-9) -67056686*a(n-10) +103057344*a(n-11) -129153505*a(n-12) +131275346*a(n-13) -107173068*a(n-14) +69203560*a(n-15) -34519952*a(n-16) +12821856*a(n-17) -3336768*a(n-18) +542592*a(n-19) -41472*a(n-20) for n>28

A250671 Number of (n+1)X(3+1) 0..3 arrays with nondecreasing 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

3927, 42422, 388916, 3107446, 22408818, 148821788, 923242475, 5408914174, 30183160828, 161540947652, 833948226614, 4172559026594, 20315088999198, 96576921782616, 449613162886204, 2055003400985552, 9241542539124820

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Column 3 of A250676

			Some solutions for n=2
..2..1..0..2....0..0..1..1....2..1..0..0....1..2..0..2....1..1..0..3
..2..1..1..1....0..0..1..2....2..1..2..3....0..3..2..0....1..1..0..3
..2..2..2..2....1..2..3..0....3..0..3..2....1..2..3..1....2..0..1..2

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

Empirical: a(n) = 65*a(n-1) -2040*a(n-2) +41182*a(n-3) -601025*a(n-4) +6757461*a(n-5) -60904682*a(n-6) +452104888*a(n-7) -2818259682*a(n-8) +14967704738*a(n-9) -68478620392*a(n-10) +272205579828*a(n-11) -946422923082*a(n-12) +2893259719938*a(n-13) -7808288819292*a(n-14) +18659986712520*a(n-15) -39573170147037*a(n-16) +74582440486893*a(n-17) -125002834972016*a(n-18) +186317017612318*a(n-19) -246795421123605*a(n-20) +290111846304617*a(n-21) -301991734906378*a(n-22) +277530162730704*a(n-23) -224266440175648*a(n-24) +158524442376560*a(n-25) -97366518380640*a(n-26) +51522457118080*a(n-27) -23231309452544*a(n-28) +8797779121920*a(n-29) -2744576054784*a(n-30) +686513332224*a(n-31) -132324212736*a(n-32) +18444423168*a(n-33) -1654235136*a(n-34) +71663616*a(n-35) for n>47

A250672 Number of (n+1)X(4+1) 0..3 arrays with nondecreasing 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

22119, 329226, 4008211, 41503790, 379890972, 3135539502, 23739860017, 167047195040, 1103768366168, 6905919873166, 41196085958108, 235655369716800, 1298966090014725, 6928230529332792, 35884432642746405, 181050004787559210

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Column 4 of A250676

			Some solutions for n=1
..3..3..0..3..0....2..2..2..2..0....1..1..2..2..1....0..1..0..0..3
..3..3..1..2..1....2..3..3..1..3....1..1..3..1..2....2..3..3..3..0

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 47

Empirical recurrence of order 47 (see link above)

A250673 Number of (n+1)X(5+1) 0..3 arrays with nondecreasing 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

120233, 2406972, 38224684, 505108522, 5803025694, 59036115470, 542694735983, 4574838198834, 35784917880517, 262221403119626, 1814189139876511, 11928469877179634, 74951135729008916, 452187475323346430

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Column 5 of A250676

			Some solutions for n=1
..1..3..1..0..1..1....1..2..2..2..1..0....0..2..0..3..0..3....2..3..0..1..2..0
..2..2..2..1..3..3....1..2..2..2..1..0....0..3..1..2..1..2....2..3..0..3..0..2

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 59

Empirical recurrence of order 59 (see link above)

A250674 Number of (n+1)X(6+1) 0..3 arrays with nondecreasing 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

637948, 16949262, 345255872, 5726252240, 81461365899, 1009432228498, 11161659240791, 111900180498102, 1030597712205895, 8812068752088130, 70559356373093922, 532907016216005428, 3819559062732066364

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Column 6 of A250676

			Some solutions for n=1
..0..2..2..2..2..0..1....0..3..0..0..3..0..3....0..1..0..1..2..1..2
..0..2..2..3..3..1..3....0..3..2..3..0..3..0....0..1..1..0..3..3..0

R. H. Hardin, Table of n, a(n) for n = 1..77

cp's OEIS Frontend

A250544 T(n,k) = number of (n+1)X(k+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

Extensions

A250669 Number of (n+1)X(1+1) 0..3 arrays with nondecreasing 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.

Views

Author

Keywords

Comments

Examples

Links

Formula

A250675 Number of (n+1)X(7+1) 0..3 arrays with nondecreasing 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.

Views

Author

Keywords

Comments

Examples

Links

A250677 Number of (1+1) X (n+1) 0..3 arrays with nondecreasing 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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A250683 Number of (7+1)X(n+1) 0..3 arrays with nondecreasing 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.

Views

Author

Keywords

Comments

Examples

Links

A250670 Number of (n+1)X(2+1) 0..3 arrays with nondecreasing 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.

Views

Author

Keywords

Comments

Examples

Links

Formula

A250671 Number of (n+1)X(3+1) 0..3 arrays with nondecreasing 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.

Views

Author

Keywords

Comments

Examples

Links

Formula

A250672 Number of (n+1)X(4+1) 0..3 arrays with nondecreasing 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.

Views

Author

Keywords

Comments

Examples

Links

Formula

A250673 Number of (n+1)X(5+1) 0..3 arrays with nondecreasing 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.

Views

Author

Keywords

Comments

Examples

Links

Formula

A250674 Number of (n+1)X(6+1) 0..3 arrays with nondecreasing 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.

Views

Author

Keywords

Comments

Examples