A252828 -id:A252828 - cp's OEIS frontend

A252821 Number of n X n nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

1, 6, 81, 1920, 54376, 1679072, 55960651, 2001017650, 76084625352, 3047083917080, 127445868976818, 5528160760257164, 247294135503496534, 11357522219262644466, 533619846702969331737, 25573797311727396663076

Offset: 1

R. H. Hardin, Dec 22 2014

nonn

Diagonal of A252828

			Some solutions for n=4
..0..1..2..3....0..1..1..2....0..1..1..2....0..1..2..3....0..1..2..2
..0..1..2..3....0..1..2..3....0..1..1..2....1..2..3..4....0..1..2..2
..1..2..3..4....1..2..3..3....0..1..2..3....2..3..3..4....1..2..3..3
..2..3..4..5....2..2..3..4....1..2..2..3....3..4..4..5....2..3..3..3

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

A252822 Number of n X 2 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

Original entry on oeis.org

2, 6, 18, 53, 142, 339, 729, 1437, 2638, 4568, 7536, 11937, 18266, 27133, 39279, 55593, 77130, 105130, 141038, 186525, 243510, 314183, 401029, 506853, 634806, 788412, 971596, 1188713, 1444578, 1744497, 2094299, 2500369, 2969682, 3509838, 4129098

Offset: 1

R. H. Hardin, Dec 22 2014

nonn

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

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

Column 2 of A252828.

Empirical: a(n) = (1/720)*n^6 + (7/240)*n^5 + (5/144)*n^4 - (11/48)*n^3 + (527/360)*n^2 - (3/10)*n + 1.
Conjectures from Colin Barker, Dec 06 2018: (Start)
G.f.: x*(2 - 8*x + 18*x^2 - 17*x^3 + 9*x^4 - 4*x^5 + 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)

A252823 Number of n X 3 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

Original entry on oeis.org

4, 18, 81, 340, 1238, 3891, 10761, 26764, 60988, 129236, 257653, 487744, 883142, 1538541, 2591269, 4236040, 6743492, 10483190, 15951849, 23807612, 34911302, 50375655, 71623633, 100457012, 139136540, 190475064, 257945133, 345802696

Offset: 1

R. H. Hardin, Dec 22 2014

nonn

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

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

Column 3 of A252828.

Empirical: a(n) = (1/90720)*n^9 + (1/2520)*n^8 + (19/3780)*n^7 + (1/45)*n^6 + (157/4320)*n^5 + (31/180)*n^4 + (28507/45360)*n^3 + (769/2520)*n^2 + (1783/630)*n.
Conjectures from Colin Barker, Dec 06 2018: (Start)
G.f.: x*(4 - 22*x + 81*x^2 - 140*x^3 + 163*x^4 - 137*x^5 + 75*x^6 - 23*x^7 + 3*x^8) / (1 - x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
(End)

A252824 Number of n X 4 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

Original entry on oeis.org

8, 53, 340, 1920, 9075, 36292, 125892, 387849, 1082111, 2777103, 6637625, 14922949, 31813809, 64737785, 126429330, 238046837, 433778614, 767506845, 1322268502, 2223460226, 3656986483, 5893853502, 9323072932, 14495166797, 22179067861

Offset: 1

R. H. Hardin, Dec 22 2014

nonn

Column 4 of A252828.

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

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

Cf. A252828.

Empirical: a(n) = (29/479001600)*n^12 + (29/8870400)*n^11 + (3083/43545600)*n^10 + (233/290304)*n^9 + (75539/14515200)*n^8 + (56551/2419200)*n^7 + (4051409/43545600)*n^6 + (123049/483840)*n^5 + (5473861/10886400)*n^4 + (1817149/1814400)*n^3 + (5653001/1663200)*n^2 + (23839/13860)*n + 1.

A252825 Number of nX5 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

Original entry on oeis.org

15, 142, 1238, 9075, 54376, 271846, 1165921, 4396009, 14863460, 45791493, 130210765, 345350438, 861722537, 2037396931, 4591832266, 9915068062, 20600380173, 41336047432, 80360448168, 151781791285, 279198974102

Offset: 1

R. H. Hardin, Dec 22 2014

nonn

Column 5 of A252828

			Some solutions for n=4
..0..1..1..2..3....0..1..1..2..2....0..1..2..3..3....0..1..2..2..2
..1..2..2..3..3....0..1..1..2..3....1..2..3..3..3....1..1..2..2..3
..2..2..3..3..3....1..1..1..2..3....1..2..3..4..4....1..2..3..3..4
..3..3..3..4..4....1..2..2..3..4....1..2..3..4..4....2..3..4..4..5

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

Empirical: a(n) = (29/130767436800)*n^15 + (29/1743565824)*n^14 + (761/1437004800)*n^13 + (4567/479001600)*n^12 + (156803/1437004800)*n^11 + (467/537600)*n^10 + (4895111/914457600)*n^9 + (8221817/304819200)*n^8 + (969313/9331200)*n^7 + (3241009/10886400)*n^6 + (129913907/179625600)*n^5 + (29795933/19958400)*n^4 + (1495061807/454053600)*n^3 + (185734933/50450400)*n^2 + (148987/27720)*n

A252826 Number of nX6 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

Original entry on oeis.org

26, 339, 3891, 36292, 271846, 1679072, 8807722, 40232545, 163307844, 598768118, 2009666884, 6242686351, 18111918515, 49456857086, 127928520595, 315195592486, 743219906659, 1684034391078, 3679765581966, 7778027858175, 15947032415637

Offset: 1

R. H. Hardin, Dec 22 2014

nonn

Column 6 of A252828

			Some solutions for n=4
..0..1..2..3..3..3....0..1..2..3..3..3....0..0..1..2..2..2....0..1..1..1..1..2
..1..2..3..3..4..4....1..1..2..3..3..3....1..1..2..2..2..3....0..1..2..2..2..3
..1..2..3..4..4..4....1..2..3..3..4..4....1..1..2..3..3..4....1..2..2..3..3..4
..2..3..4..5..5..5....2..3..3..4..5..5....1..2..3..4..4..5....2..2..3..4..4..5

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

Empirical: a(n) = (883/1600593426432000)*n^18 + (883/16167610368000)*n^17 + (148963/62768369664000)*n^16 + (6599/108972864000)*n^15 + (8020459/7846046208000)*n^14 + (3062099/249080832000)*n^13 + (813736283/7242504192000)*n^12 + (166116079/201180672000)*n^11 + (1097726573/219469824000)*n^10 + (598115773/24385536000)*n^9 + (466445792503/4828336128000)*n^8 + (272090281/870912000)*n^7 + (19554578278049/23538138624000)*n^6 + (1173600978721/653837184000)*n^5 + (4602055984369/1307674368000)*n^4 + (98334957191/18162144000)*n^3 + (263932729939/30875644800)*n^2 + (3637273/816816)*n + 1

A252827 Number of n X 7 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

Original entry on oeis.org

42, 729, 10761, 125892, 1165921, 8807722, 55960651, 306796310, 1481748658, 6411737114, 25203579317, 91037124979, 305083525901, 956286103952, 2823092600299, 7895877354183, 21029532417878, 53571661955209

Offset: 1

R. H. Hardin, Dec 22 2014

nonn

Column 7 of A252828.

			Some solutions for n=4
..0..1..2..2..3..4..4....0..1..2..3..3..4..5....0..1..2..3..3..4..5
..1..2..3..3..4..5..5....0..1..2..3..4..5..5....1..2..3..3..4..5..5
..1..2..3..4..4..5..5....1..1..2..3..4..5..5....1..2..3..4..5..5..6
..2..3..4..5..5..6..6....1..2..3..3..4..5..6....2..3..4..4..5..5..6

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

Cf. A252828.

Empirical: a(n) = (491/510909421717094400)*n^21 + (491/4054836680294400)*n^20 + (31237/4561691265331200)*n^19 + (16931/72754246656000)*n^18 + (6860417/1280474741145600)*n^17 + (5620079/62768369664000)*n^16 + (28238557/24715045555200)*n^15 + (460207/39626496000)*n^14 + (1996189759/20542375526400)*n^13 + (9849852413/14485008384000)*n^12 + (262128023/65840947200)*n^11 + (23507656471/1207084032000)*n^10 + (126607207245823/1581762915532800)*n^9 + (1573022155907/5706215424000)*n^8 + (887749472755/1129830653952)*n^7 + (43972723546711/23538138624000)*n^6 + (101853364790929/26676557107200)*n^5 + (13152985155929/2020951296000)*n^4 + (11601438763393/1119943843200)*n^3 + (5765297083043/586637251200)*n^2 + (131188073/15519504)*n.

cp's OEIS Frontend

A252821 Number of n X n nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

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A252822 Number of n X 2 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

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A252823 Number of n X 3 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

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A252824 Number of n X 4 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

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A252825 Number of nX5 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

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A252826 Number of nX6 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

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A252827 Number of n X 7 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

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