A224281 -id:A224281 - cp's OEIS frontend

A224276 Number of nX3 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

50, 984, 13683, 186516, 2596992, 37128051, 537465766, 7804602744, 113382138975, 1646661944858, 23908590491858, 347099092628781, 5038892410726190, 73149786094975076, 1061918636087967819, 15415943271255819642

Offset: 1

R. H. Hardin Apr 02 2013

nonn

Column 3 of A224281

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

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

Empirical: a(n) = 20*a(n-1) -70*a(n-2) -211*a(n-3) +192*a(n-4) +15174*a(n-5) -36608*a(n-6) -83340*a(n-7) +59774*a(n-8) +2310958*a(n-9) -3620776*a(n-10) -5846720*a(n-11) +390652*a(n-12) +87932540*a(n-13) -70516876*a(n-14) +46329332*a(n-15) +7472696*a(n-16) -557612816*a(n-17) +319521288*a(n-18) -63018416*a(n-19) +17463360*a(n-20) +1046997696*a(n-21) -323677440*a(n-22) -14515200*a(n-23) -56540160*a(n-24) -635904000*a(n-25) for n>26

A224277 Number of nX4 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

130, 4580, 84132, 1334973, 21348990, 356222482, 6172817040, 109166159263, 1947747629183, 34864494529806, 624634228911233, 11192898789327524, 200562963738597382, 3593689853465024489, 64389966977277732381

Offset: 1

R. H. Hardin Apr 02 2013

nonn

Column 4 of A224281

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 52

Empirical recurrence of order 52 (see link above)

A224278 Number of nX5 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

296, 17723, 442089, 8073038, 137489538, 2425304290, 45275725025, 883012703273, 17667432461262, 358042017265316, 7298750316970616, 149179000331610043, 3052840234754205390, 62514535525552969948, 1280625241031012026560

Offset: 1

R. H. Hardin Apr 02 2013

nonn

Column 5 of A224281

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

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

A224279 Number of nX6 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

610, 59792, 2059793, 44901359, 817075668, 14587480744, 274116529912, 5481124776302, 115036474923900, 2489043013161042, 54774515108860284, 1216015762754882736, 27117272628943751854, 606168132402047719588

Offset: 1

R. H. Hardin Apr 02 2013

nonn

Column 6 of A224281

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

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

A224280 Number of nX7 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

1163, 180821, 8626382, 233090092, 4728056658, 86539248276, 1597855917875, 31198793873704, 648539832987579, 14190379537730766, 321738654013526452, 7458658599338643026, 175162125039011466648, 4143668812111247607851

Offset: 1

R. H. Hardin Apr 02 2013

nonn

Column 7 of A224281

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

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

A224282 Number of 3Xn 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

64, 1600, 13683, 84132, 442089, 2059793, 8626382, 32788075, 114177368, 367630559, 1103854119, 3114501259, 8312578140, 21108455323, 51251494995, 119493052710, 268514504126, 583406544627, 1229033304669, 2516545359868, 5019124209561

Offset: 1

R. H. Hardin Apr 02 2013

nonn

Row 3 of A224281

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

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

Empirical: a(n) = (1/3629463552000)*n^18 + (1/80654745600)*n^17 + (1123/2092278988800)*n^16 + (37607/2615348736000)*n^15 + (1660537/5230697472000)*n^14 + (58097/11496038400)*n^13 + (870097/11496038400)*n^12 + (18766109/28740096000)*n^11 + (404719067/73156608000)*n^10 + (535345591/14631321600)*n^9 + (24473380931/160944537600)*n^8 + (549661909/449064000)*n^7 + (1232106541/768768000)*n^6 + (74468938879/3736212480)*n^5 + (59979142753/8717829120)*n^4 + (521837272841/9081072000)*n^3 + (1774626948209/5145940800)*n^2 - (140683661/117810)*n + 1114 for n>3

A224283 Number of 4Xn 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

256, 16000, 186516, 1334973, 8073038, 44901359, 233090092, 1121852243, 4979825221, 20391024279, 77331512406, 273217833082, 905042600151, 2828381836611, 8387049692461, 23720147714267, 64273739402314

Offset: 1

R. H. Hardin Apr 02 2013

nonn

Row 4 of A224281

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

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

Empirical: a(n) = (1/2906843957821440000)*n^24 + (1/80745665495040000)*n^23 + (46391/53523844179886080000)*n^22 + (11257/405483668029440000)*n^21 + (1330123/1390229718958080000)*n^20 + (8502743/347557429739520000)*n^19 + (35671/59779399680000)*n^18 + (133834769/10670622842880000)*n^17 + (7571063047/30128817438720000)*n^16 + (2965237343/836911595520000)*n^15 + (328422846067/15064408719360000)*n^14 + (22514281381/48910417920000)*n^13 + (7036550185081/2254537359360000)*n^12 - (105103493973601/2510734786560000)*n^11 + (1257210817095943/1076029194240000)*n^10 - (236735071681049/19615115520000)*n^9 + (3534310707922188979/32011868528640000)*n^8 - (767055210116438233/1143281018880000)*n^7 + (10350657608308971137/3103191336960000)*n^6 - (8154723578394294443/703964701440000)*n^5 + (16475873524529520931/527973526080000)*n^4 - (482012437494247/8888443200)*n^3 + (78892730856408401/873054262080)*n^2 - (77283877096589/243374040)*n + 643573 for n>7

A224284 Number of 5Xn 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

1024, 160000, 2596992, 21348990, 137489538, 817075668, 4728056658, 26524273813, 141437578159, 706256665798, 3280530467805, 14165878265784, 57028400060821, 214999615263699, 762959963267749, 2561695629991349, 8178284227377456

Offset: 1

R. H. Hardin Apr 02 2013

nonn

Row 5 of A224281

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical polynomial of degree 30

Empirical polynomial of degree 30 (see link above)

A224285 Number of 6Xn 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

4096, 1600000, 37128051, 356222482, 2425304290, 14587480744, 86539248276, 519675953580, 3101250505830, 17906548084860, 98091759991859, 504379639489778, 2424565118584031, 10897029351109181, 45902682124075154

Offset: 1

R. H. Hardin Apr 02 2013

nonn

Row 6 of A224281

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

R. H. Hardin, Table of n, a(n) for n = 1..102
R. H. Hardin, Empirical polynomial of degree 36

Empirical polynomial of degree 36 (see link above)

A224286 Number of 7Xn 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

16384, 16000000, 537465766, 6172817040, 45275725025, 274116529912, 1597855917875, 9622753439382, 59980603070388, 376494813177039, 2313407919278369, 13634051825496929, 76116429236458083, 400003671053134168

Offset: 1

R. H. Hardin Apr 02 2013

nonn

Row 7 of A224281

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

R. H. Hardin, Table of n, a(n) for n = 1..46

cp's OEIS Frontend

A224276 Number of nX3 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224277 Number of nX4 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224278 Number of nX5 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224279 Number of nX6 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224280 Number of nX7 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224282 Number of 3Xn 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224283 Number of 4Xn 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224284 Number of 5Xn 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224285 Number of 6Xn 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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A224286 Number of 7Xn 0..3 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

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