A223762 -id:A223762 - cp's OEIS frontend

A223756 Number of n X 2 0..3 arrays with rows, antidiagonals and columns unimodal.

16, 256, 2500, 16900, 87616, 372100, 1352569, 4338889, 12559936, 33362176, 82373776, 190992400, 419266576, 877225924, 1759047481, 3396208729, 6338070544, 11471266816, 20192978404, 34657779556, 58123423744, 95427859396

Offset: 1

R. H. Hardin, Mar 27 2013

nonn

Column 2 of A223762.

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

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

Empirical: a(n) = (1/518400)*n^12 + (1/17280)*n^11 + (91/103680)*n^10 + (71/8640)*n^9 + (9101/172800)*n^8 + (457/1920)*n^7 + (81397/103680)*n^6 + (497/270)*n^5 + (203687/64800)*n^4 + (1933/540)*n^3 + (2533/720)*n^2 + (11/6)*n + 1.
a(n) = A223659(n)^2. - Mark van Hoeij, May 14 2013
Conjectures from Colin Barker, Feb 19 2018: (Start)
G.f.: x*(16 + 48*x + 420*x^2 - 208*x^3 + 1140*x^4 - 1260*x^5 + 1401*x^6 - 1044*x^7 + 597*x^8 - 244*x^9 + 69*x^10 - 12*x^11 + x^12) / (1 - x)^13.
a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13) for n>13.
(End)

A223757 Number of nX3 0..3 arrays with rows, antidiagonals and columns unimodal.

Original entry on oeis.org

50, 2500, 61733, 916107, 9478535, 74824917, 477860225, 2571238699, 12006271464, 49749360288, 186123469150, 637408917764, 2020521264556, 5982701793264, 16672986760595, 44013068603319, 110650947588800, 266164581427718

Offset: 1

R. H. Hardin Mar 27 2013

nonn

Column 3 of A223762

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

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

Empirical: a(n) = (89/169374965760)*n^18 + (673039/29640619008000)*n^17 + (5753323/10461394944000)*n^16 + (20639/2335132800)*n^15 + (5460977/52306974720)*n^14 + (350675333/373621248000)*n^13 + (34569853/5225472000)*n^12 + (744079211/20118067200)*n^11 + (1214093389/7315660800)*n^10 + (3120210973/5225472000)*n^9 + (1381865894063/804722688000)*n^8 + (2224350329/574801920)*n^7 + (252375235967/37362124800)*n^6 + (1486577243227/163459296000)*n^5 + (2159143550149/217945728000)*n^4 + (154699301/14414400)*n^3 - (959722661/467812800)*n^2 + (50040773/6126120)*n + 1

A223758 Number of nX4 0..3 arrays with rows, antidiagonals and columns unimodal.

Original entry on oeis.org

130, 16900, 916107, 26631193, 499583168, 6754232986, 70657105931, 600526842770, 4295532642860, 26553802745045, 144809883138117, 708169972948277, 3147072278088124, 12848530197514221, 48634231381716779, 171996928938851128

Offset: 1

R. H. Hardin Mar 27 2013

nonn

Column 4 of A223762

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

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

Empirical: a(n) = (1224989653/34469355651846635520000)*n^24 + (49730855441/25852016738884976640000)*n^23 + (333257/5098722951168000)*n^22 + (26404629869/17030314057236480000)*n^21 + (15548385067/556091887583232000)*n^20 + (27895851209/69844076789760000)*n^19 + (413849303311/89633231880192000)*n^18 + (59360314638299/1344498478202880000)*n^17 + (77412356681/219118672281600)*n^16 + (251034590870443/105450861035520000)*n^15 + (898424139706433/66283398365184000)*n^14 + (16142406345876497/248562743869440000)*n^13 + (9698986684015669/37118703084503040)*n^12 + (278016346455319699/316352583106560000)*n^11 + (583356258129599/231760134144000)*n^10 + (1085396771654087/199717539840000)*n^9 + (179557726299779059/12804747411456000)*n^8 + (170830900302526489/48017802792960000)*n^7 + (27511312022727679/455355990835200)*n^6 - (2749822055519840233/88699552381440000)*n^5 - (122655525295200187/1222675534080000)*n^4 + (309022440348259051/271026410054400)*n^3 - (60572016509105077/18552403069200)*n^2 + (285878479129/70450380)*n - 1588 for n>2

A223759 Number of nX5 0..3 arrays with rows, antidiagonals and columns unimodal.

Original entry on oeis.org

296, 87616, 9478535, 499583168, 15947472102, 350182483445, 5733827943118, 73972033945807, 782389879664731, 6990377642784235, 54000675009376965, 367428839857095864, 2235505630899285226, 12314718611480572990

Offset: 1

R. H. Hardin Mar 27 2013

nonn

Column 5 of A223762

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

R. H. Hardin, Table of n, a(n) for n = 1..77

Empirical: a(n) = (12185409283/15043832793341144432640000000)*n^30 + (27923308904923/552610124608731372158976000000)*n^29 + (17202351123943/7559215155662327119872000000)*n^28 + (83889482659651/1146196784254563385344000000)*n^27 + (131580424853251541/72592463002789014405120000000)*n^26 + (91300610653453/2481793606932957757440000)*n^25 + (2869131224226844253/4690589917103290161561600000)*n^24 + (6733459014124696993/781764986183881693593600000)*n^23 + (105395815298504753443/1019693460239845687296000000)*n^22 + (470586110891157493/441425740363569561600000)*n^21 + (92313858824481506713/9711366287998530355200000)*n^20 + (40366817013100567291/539520349333251686400000)*n^19 + (2857208469478310355787/5765991728193994752000000)*n^18 + (73804544320284819569293/23256166637049112166400000)*n^17 + (105623541268201591322087/8208058813076157235200000)*n^16 + (20778860285663090466941/195429971739908505600000)*n^15 - (4122006232669364727200509/33223095195784445952000000)*n^14 + (14082517009271704071311/3155089762182758400000)*n^13 - (182553094899048464076429353/8050211528209308057600000)*n^12 + (351832338444643788138816403/2317485136908740198400000)*n^11 - (636192073310304596009591323513/955962618974855331840000000)*n^10 + (673686037713545840541517207/239589628815753216000000)*n^9 - (507622569326119951528072091/48071931952472064000000)*n^8 + (33298798403375782384332287329/969450627708186624000000)*n^7 - (2608160997837482966479278684073/36758336300602076160000000)*n^6 + (3318743520542516326928702347/122527787668673587200000)*n^5 + (519721318997776322417985167/6126389383433679360000)*n^4 + (8189409887763024441897379/7293320694563904000)*n^3 - (52484216692264826985673/9647249595984000)*n^2 + (2840122633336908109/465817912560)*n + 2746822 for n>5

A223760 Number of nX6 0..3 arrays with rows, antidiagonals and columns unimodal.

Original entry on oeis.org

610, 372100, 74824917, 6754232986, 350182483445, 12025063773557, 298630624023222, 5692159574625373, 86933612444360250, 1098959847553820404, 11794801172063561487, 109687177820504204805, 898680887461860405330

Offset: 1

R. H. Hardin Mar 27 2013

nonn

Column 6 of A223762

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

R. H. Hardin, Table of n, a(n) for n = 1..16

A223755 Number of n X n 0..3 arrays with rows, antidiagonals and columns unimodal.

Original entry on oeis.org

4, 256, 61733, 26631193, 15947472102, 12025063773557, 10962346407561257, 11777774040586957640

Offset: 1

R. H. Hardin Mar 27 2013

nonn

Diagonal of A223762

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

A223761 Number of nX7 0..3 arrays with rows, antidiagonals and columns unimodal.

Original entry on oeis.org

1163, 1352569, 477860225, 70657105931, 5733827943118, 298630624023222, 10962346407561257, 301938629597593741, 6529314611297747401, 114748898336983659524

Offset: 1

R. H. Hardin Mar 27 2013

nonn

Column 7 of A223762

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

cp's OEIS Frontend

A223756 Number of n X 2 0..3 arrays with rows, antidiagonals and columns unimodal.

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A223757 Number of nX3 0..3 arrays with rows, antidiagonals and columns unimodal.

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A223758 Number of nX4 0..3 arrays with rows, antidiagonals and columns unimodal.

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A223759 Number of nX5 0..3 arrays with rows, antidiagonals and columns unimodal.

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A223760 Number of nX6 0..3 arrays with rows, antidiagonals and columns unimodal.

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A223755 Number of n X n 0..3 arrays with rows, antidiagonals and columns unimodal.

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A223761 Number of nX7 0..3 arrays with rows, antidiagonals and columns unimodal.

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