A250691 -id:A250691 - cp's OEIS frontend

A255002 Coefficients of recurrence for rows and columns of A250544 and rows of A250691.

-1, 30, -415, 3514, -20386, 85924, -272198, 661180, -1244717, 1822478, -2068955, 1802474, -1181760, 563888, -184752, 37152, -3456

Offset: 0

M. F. Hasler, Feb 11 2015

The convention for signs and indices is such that A(n) = sum_{k=1..16} a(k)*A(n-k), where A is any row of A250691 (i.e., A250692 - A250698) or row or column of A250544 (i.e., A223069, A250538 - A250543).

Cf. A250691, A250692 - A250698; A250544, A223069, A250538 - A250543.

Vecrev(-denominator(ggf(A250538=b2v(readvec("/tmp/b250538.txt"))))) \\ using the "guess generating function" and "b-file to vector" scripts found on the OEIS wiki

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

A250692 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, 543, 2541, 11150, 47002, 193117, 780551, 3122604, 12415380, 49197371, 194657281, 769963978, 3046948238, 12068103705, 47849956731, 189941232872, 754813261576, 3002665654519, 11955693334901, 47642223194886

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Row 1 of A250691.

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

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

Cf. A250691.

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*(104 - 1121*x + 4877*x^2 - 11052*x^3 + 13756*x^4 - 8880*x^5 + 2304*x^6) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)^2*(1 - 4*x)). - Colin Barker, Feb 21 2018

A250698 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, 7249825, 37322413, 160222342, 617657415, 2224688673, 7662909389, 25622390948, 84040600357, 272488719033, 878393149045, 2826884204762, 9107833801683, 29426182298097, 95415082577317, 310574007541112

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Row 7 of A250691

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

R. H. Hardin, Table of n, a(n) for n = 1..22

Empirical: a(n) = 30*a(n-1) -415*a(n-2) +3514*a(n-3) -20386*a(n-4) +85924*a(n-5) -272198*a(n-6) +661180*a(n-7) -1244717*a(n-8) +1822478*a(n-9) -2068955*a(n-10) +1802474*a(n-11) -1181760*a(n-12) +563888*a(n-13) -184752*a(n-14) +37152*a(n-15) -3456*a(n-16)

A250693 Number of (2+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

520, 2920, 13906, 60508, 249512, 995624, 3894542, 15061244, 57914756, 222291368, 853854042, 3287692860, 12701872800, 49262782920, 191821043814, 749801489244, 2941369935292, 11575782602248, 45685412767666, 180742482085084

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Row 2 of A250691

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

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

Empirical: a(n) = 20*a(n-1) -175*a(n-2) +882*a(n-3) -2835*a(n-4) +6072*a(n-5) -8777*a(n-6) +8458*a(n-7) -5204*a(n-8) +1848*a(n-9) -288*a(n-10)

A250694 Number of (3+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

2512, 15246, 74631, 324648, 1315446, 5098590, 19218493, 71223396, 261469392, 955896790, 3493273891, 12795574192, 47067986826, 174102348110, 648137931065, 2429513706796, 9171278516740, 34862473392934, 133406490904351

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Row 3 of A250691

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

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

Empirical: a(n) = 30*a(n-1) -415*a(n-2) +3514*a(n-3) -20386*a(n-4) +85924*a(n-5) -272198*a(n-6) +661180*a(n-7) -1244717*a(n-8) +1822478*a(n-9) -2068955*a(n-10) +1802474*a(n-11) -1181760*a(n-12) +563888*a(n-13) -184752*a(n-14) +37152*a(n-15) -3456*a(n-16)

A250695 Number of (4+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

11736, 76320, 383440, 1670016, 6671458, 25235016, 92169818, 329292956, 1160994284, 4064711976, 14193722396, 49590850136, 173757950350, 611608432408, 2165540377158, 7721145553812, 27744881818344, 100541208763000

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Row 4 of A250691

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

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

Empirical: a(n) = 30*a(n-1) -415*a(n-2) +3514*a(n-3) -20386*a(n-4) +85924*a(n-5) -272198*a(n-6) +661180*a(n-7) -1244717*a(n-8) +1822478*a(n-9) -2068955*a(n-10) +1802474*a(n-11) -1181760*a(n-12) +563888*a(n-13) -184752*a(n-14) +37152*a(n-15) -3456*a(n-16)

A250696 Number of (5+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

53032, 362241, 1848953, 8038566, 31728758, 117793753, 420283865, 1461625340, 5002774320, 16967929009, 57302621481, 193328559946, 653111062242, 2212763076073, 7527314240137, 25733887423136, 88490379721660

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Row 5 of A250691

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

R. H. Hardin, Table of n, a(n) for n = 1..188

Empirical: a(n) = 30*a(n-1) -415*a(n-2) +3514*a(n-3) -20386*a(n-4) +85924*a(n-5) -272198*a(n-6) +661180*a(n-7) -1244717*a(n-8) +1822478*a(n-9) -2068955*a(n-10) +1802474*a(n-11) -1181760*a(n-12) +563888*a(n-13) -184752*a(n-14) +37152*a(n-15) -3456*a(n-16)

A250697 Number of (6+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

233300, 1647460, 8474002, 36673634, 143136866, 523260542, 1832718604, 6241479780, 20880237460, 69123618848, 227638279630, 748479312062, 2463064051982, 8124116088970, 26881398786600, 89272256311120

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Row 6 of A250691

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

R. H. Hardin, Table of n, a(n) for n = 1..55

Empirical: a(n) = 30*a(n-1) -415*a(n-2) +3514*a(n-3) -20386*a(n-4) +85924*a(n-5) -272198*a(n-6) +661180*a(n-7) -1244717*a(n-8) +1822478*a(n-9) -2068955*a(n-10) +1802474*a(n-11) -1181760*a(n-12) +563888*a(n-13) -184752*a(n-14) +37152*a(n-15) -3456*a(n-16)

A250685 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

543, 2920, 15246, 76320, 362241, 1647460, 7249825, 31113316, 131014715, 543845812, 2233368847, 9098214240, 36844025643, 148553970588, 597082293823, 2394504059784, 9587995012203, 38352450171812, 153311305422383

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Column 2 of A250691

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

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

Empirical: a(n) = 27*a(n-1) -331*a(n-2) +2439*a(n-3) -12049*a(n-4) +42129*a(n-5) -107225*a(n-6) +201069*a(n-7) -277706*a(n-8) +278928*a(n-9) -197984*a(n-10) +94032*a(n-11) -26784*a(n-12) +3456*a(n-13) for n>17

cp's OEIS Frontend

A255002 Coefficients of recurrence for rows and columns of A250544 and rows of A250691.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

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

A250692 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

A250698 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

Formula

A250693 Number of (2+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

Formula

A250694 Number of (3+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

Formula

A250695 Number of (4+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

Formula

A250696 Number of (5+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

Formula

A250697 Number of (6+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

Formula

A250685 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