A223071 -id:A223071 - 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

A223069 Number of n X 2 0..3 arrays with successive rows and columns fitting to straight lines with nondecreasing slope, with a single point array taken as having zero slope.

Original entry on oeis.org

16, 150, 1080, 6627, 36552, 187000, 905440, 4206453, 18933408, 83153850, 358250280, 1520208679, 6373759384, 26468569500, 109080982800, 446806304505, 1821267503280, 7395000190750, 29933239010200, 120863093617131

Offset: 1

R. H. Hardin; Mar 14 2013

nonn

Column 2 of A223071.

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

R. H. Hardin, Table of n, a(n) for n = 1..41

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).

Empirical g.f.: x*(16 - 106*x + 376*x^2 - 769*x^3 + 904*x^4 - 564*x^5 + 144*x^6) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)^2*(1 - 4*x)). - Colin Barker, Feb 18 2018

A223070 Number of nX3 0..3 arrays with successive rows and columns fitting to straight lines with nondecreasing slope, with a single point array taken as having zero slope.

Original entry on oeis.org

64, 1080, 38512, 899390, 22520656, 462313688, 9567328752, 178464221290, 3336648010448, 58641450033936, 1033599371410096, 17499076161248060, 297470720803662048, 4917593684170711306, 81699455573347788176

Offset: 1

R. H. Hardin Mar 14 2013

nonn

Column 3 of A223071

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

R. H. Hardin, Table of n, a(n) for n = 1..25

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.

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A223069 Number of n X 2 0..3 arrays with successive rows and columns fitting to straight lines with nondecreasing slope, with a single point array taken as having zero slope.

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A223070 Number of nX3 0..3 arrays with successive rows and columns fitting to straight lines with nondecreasing slope, with a single point array taken as having zero slope.

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Author

Keywords

Comments

Examples

Links