A250669 -id:A250669 - cp's OEIS frontend

A250691 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 absolute value of x(i,j)-x(i-1,j) in the j direction.

104, 543, 520, 2541, 2920, 2512, 11150, 13906, 15246, 11736, 47002, 60508, 74631, 76320, 53032, 193117, 249512, 324648, 383440, 362241, 233300, 780551, 995624, 1315446, 1670016, 1848953, 1647460, 1005121, 3122604, 3894542, 5098590, 6671458

Offset: 1

R. H. Hardin, Nov 26 2014

Table starts
......104.......543.......2541.......11150.......47002......193117......780551
......520......2920......13906.......60508......249512......995624.....3894542
.....2512.....15246......74631......324648.....1315446.....5098590....19218493
....11736.....76320.....383440.....1670016.....6671458....25235016....92169818
....53032....362241....1848953.....8038566....31728758...117793753...420283865
...233300...1647460....8474002....36673634...143136866...523260542..1832718604
..1005121...7249825...37322413...160222342...617657415..2224688673..7662909389
..4260728..31113316..159438246...676640344..2571646112..9121206688.30911828018
.17835379.131014715..665575403..2784280670.10412478449.36332194553
.73930174.543845812.2731006288.11235235268.41269021168

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

R. H. Hardin, Table of n, a(n) for n = 1..112

Column 1 is A250669.

Rows 1-7 are A250692, ..., A250698.

Empirical for column k:
k=1: [linear recurrence of order 7] for n>11
k=2: [order 13] for n>17
k=3: [same order 13] for n>17
k=4: [same order 13] for n>17
k=5: [same order 13] for n>17
k=6: [same order 13] for n>17
k=7: [same order 13] for n>17
Empirical for row n:
n=1: [linear recurrence of order 7, cf. A250692]
n=2: [order 10, cf. A250693]
n=3: [order 16, cf. A250694]
n=4: [same order 16, cf. A250695]
n=5: [same order 16, cf. A250696]
n=6: [same order 16, cf. A250697]
n=7: [same order 16, cf. A250698].

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.

Original entry on oeis.org

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

cp's OEIS Frontend

A250691 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 absolute value of x(i,j)-x(i-1,j) in the j direction.

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