A223801 -id:A223801 - cp's OEIS frontend

A223795 Number of n X n 0..3 arrays with rows and antidiagonals unimodal.

4, 256, 110116, 151310069, 453578376041, 2401987689157097, 19618352087687868206, 225161556703631799074083, 3396567436573176749810085543, 64088930629934993395801694394536

Offset: 1

R. H. Hardin Mar 27 2013

nonn

Diagonal of A223801

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

R. H. Hardin, Table of n, a(n) for n = 1..11

A223796 Number of nX3 0..3 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

50, 2500, 110116, 4816168, 210163664, 9169032476, 400006582368, 17450517286804, 761287955888788, 33211580867804324, 1448872354425344280, 63207803924281966208, 2757473052802943936172, 120296184397162010680224

Offset: 1

R. H. Hardin Mar 27 2013

nonn

Column 3 of A223801

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

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

Empirical: a(n) = 50*a(n-1) -253*a(n-2) -1283*a(n-3) +8456*a(n-4) -10020*a(n-5) -12064*a(n-6) +27360*a(n-7) -6656*a(n-8) -9728*a(n-9) +4096*a(n-10)

A223797 Number of nX4 0..3 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

130, 16900, 1658703, 151310069, 13602542576, 1216562667529, 108631485025292, 9695922803812530, 865293308203272685, 77218182866179219113, 6890814828420641198100, 614921940899081513160269

Offset: 1

R. H. Hardin Mar 27 2013

nonn

Column 4 of A223801

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

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

Empirical: a(n) = 130*a(n-1) -4151*a(n-2) +55367*a(n-3) -1103289*a(n-4) +25676564*a(n-5) -311713584*a(n-6) +2153547070*a(n-7) -14084700670*a(n-8) +111538734736*a(n-9) -678666743150*a(n-10) +3151156493032*a(n-11) -15705615808280*a(n-12) +74227237529348*a(n-13) -265525650225285*a(n-14) +858145104057893*a(n-15) -2835818034237058*a(n-16) +7784228337705693*a(n-17) -17375928755819704*a(n-18) +37062908059029592*a(n-19) -69764230981154356*a(n-20) +99762651233668576*a(n-21) -119132184363098064*a(n-22) +127177566453563712*a(n-23) -90807087696380928*a(n-24) +28396177139635200*a(n-25) -1473691515457536*a(n-26) +18962192793600*a(n-27)

A223798 Number of n X 5 0..3 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

296, 87616, 16979881, 2844578252, 453578376041, 70950413903439, 11005258705825234, 1701108873516414461, 262573419115915016653, 40505547476599298757032, 6247008370524009857378298

Offset: 1

R. H. Hardin, Mar 27 2013

nonn

Column 5 of A223801.

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

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

Cf. A223801.

A223799 Number of nX6 0..3 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

610, 372100, 131295500, 37217420249, 9658691177678, 2401987689157097, 584566278788358762, 140706704179577280652, 33682261034207872011248, 8040572062005220287891916, 1916764185795334806820505504

Offset: 1

R. H. Hardin Mar 27 2013

nonn

Column 6 of A223801

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

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

A223800 Number of nX7 0..3 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

1163, 1352569, 818316500, 370255807510, 147492079608804, 54863639440148543, 19618352087687868206, 6858114712379977473803, 2366525095854843153846166, 810568137864555472117760103, 276450663558980453778169837060

Offset: 1

R. H. Hardin Mar 27 2013

nonn

Column 7 of A223801

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

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

A223802 Number of 3Xn 0..3 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

64, 4096, 110116, 1658703, 16979881, 131295500, 818316500, 4293683039, 19561009057, 79169569680, 289707943960, 971844411710, 3021916484046, 8789182733640, 24090737306249, 62620436201529, 155188103218258

Offset: 1

R. H. Hardin Mar 27 2013

nonn

Row 3 of A223801

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

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

Empirical: a(n) = (89/169374965760)*n^18 + (811/30536352000)*n^17 + (94651/130767436800)*n^16 + (32953/2554051500)*n^15 + (353321/2134978560)*n^14 + (42487607/26687232000)*n^13 + (2427919/205286400)*n^12 + (329331899/4790016000)*n^11 + (2304632003/7315660800)*n^10 + (10342060619/9144576000)*n^9 + (4533016361/1437004800)*n^8 + (13748687149/2052864000)*n^7 + (50457321263/4670265600)*n^6 + (22295176297/1796256000)*n^5 + (1377479947/136216080)*n^4 + (30053444821/9081072000)*n^3 + (2978057767/367567200)*n^2 + (16725/2431)*n + 1

A223803 Number of 4Xn 0..3 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

256, 65536, 4816168, 151310069, 2844578252, 37217420249, 370255807510, 2967702264487, 19953618004020, 115901407902175, 594677748128499, 2742258352954012, 11522283571283326, 44607717280309708, 160585424830894289

Offset: 1

R. H. Hardin Mar 27 2013

nonn

Row 4 of A223801

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

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

Empirical: a(n) = (1224989653/34469355651846635520000)*n^24 + (1274345773/470036667979726848000)*n^23 + (89684176061/749333818518405120000)*n^22 + (92332596599/25545471085854720000)*n^21 + (3678754549/45368802017280000)*n^20 + (80494587659/57244753133568000)*n^19 + (1442890795373/74694359900160000)*n^18 + (17944065812311/84031154887680000)*n^17 + (808497136964749/421803444142080000)*n^16 + (887979405310979/63270516621312000)*n^15 + (712542665498819/8497871585280000)*n^14 + (511835344841201/1255367393280000)*n^13 + (2484047083210032763/1546612628520960000)*n^12 + (29342532497594837/5751865147392000)*n^11 + (124717183755287231/9586441912320000)*n^10 + (524203224847641397/19772036444160000)*n^9 + (23382114961946647/547211427840000)*n^8 + (33110696329013011/640237370572800)*n^7 + (78034921690145238953/2128789257154560000)*n^6 - (394245218967404573/9855505820160000)*n^5 - (11421559789359613027/81307923016320000)*n^4 - (57003741297203/301945644000)*n^3 + (2875733400346871/11416863427200)*n^2 + (225454400125/1070845776)*n - 15

A223804 Number of 5Xn 0..3 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

1024, 1048576, 210163664, 13602542576, 453578376041, 9658691177678, 147492079608804, 1738265364563074, 16624933432537046, 133772722680020893, 930338345848608947, 5709392263061431701, 31428574139042436485

Offset: 1

R. H. Hardin Mar 27 2013

nonn

Row 5 of A223801

			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..2..0....0..0..0....0..0..0....0..0..0....0..2..0....0..2..0
..2..2..1....1..2..0....0..0..0....1..0..0....2..0..0....3..2..2....0..2..1
..3..1..1....1..3..2....2..3..2....3..3..0....0..2..1....2..2..2....1..3..3
..1..2..0....3..1..0....1..3..2....3..0..0....3..1..1....1..1..1....2..2..1

R. H. Hardin, Table of n, a(n) for n = 1..152

Empirical: a(n) = (12185409283/15043832793341144432640000000)*n^30 + (76296730104643/884176199373970195454361600000)*n^29 + (371907650782571/65333216702510112964608000000)*n^28 + (1151102366842559/4355547780167340864307200000)*n^27 + (338234821790386273/36296231501394507202560000000)*n^26 + (357033935267827/1378774226073865420800000)*n^25 + (13631151365462522107/2345294958551645080780800000)*n^24 + (16740679506000614867/156352997236776338718720000)*n^23 + (119233024700630228357/72835247159988977664000000)*n^22 + (263813261261433287/12612164010387701760000)*n^21 + (64065941370817311811/285628420235250892800000)*n^20 + (8076987180619121371/3996447032098160640000)*n^19 + (5334961705848505741485791/348842499555736682496000000)*n^18 + (450858411768010052623451/4651233327409822433280000)*n^17 + (300491370965924162197759/586289915219725516800000)*n^16 + (17563968862511001347771/7817198869596340224000)*n^15 + (134531017813019228073534643/16611547597892222976000000)*n^14 + (33668222196298965216433/1419790392982241280000)*n^13 + (224429158876824166363763453/4025105764104654028800000)*n^12 + (12074189473194325363982201/115874256845437009920000)*n^11 + (10894534329021783625843566583/68283044212489666560000000)*n^10 + (44842282464981860911345889/227610147374965555200000)*n^9 + (500341840567104079760229311/2908351883124559872000000)*n^8 - (6956889324683760951709681/12118132846352332800000)*n^7 - (22335181829123680152688619197/9189584075150519040000000)*n^6 - (486619909336332713379638689/61263893834336793600000)*n^5 - (1635897124538888506513/525329221697280000)*n^4 - (35225574821544661546673/7293320694563904000)*n^3 + (382682859390107193527/9647249595984000)*n^2 - (11221241883754589/465817912560)*n - 377 for n>2

A223805 Number of 6Xn 0..3 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

4096, 16777216, 9169032476, 1216562667529, 70950413903439, 2401987689157097, 54863639440148543, 926152518399324838, 12281305845727356247, 133569446404885491509, 1229947638993873947499, 9824466906501135882300

Offset: 1

R. H. Hardin Mar 27 2013

nonn

Row 6 of A223801

			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..2..0....0..2..0....0..0..0....0..2..0....0..0..0....0..0..0
..3..2..1....1..2..3....1..2..1....0..0..3....0..2..2....1..2..1....2..2..2
..0..2..3....1..2..3....3..2..0....3..3..3....1..3..3....1..1..2....1..2..0
..0..0..1....1..2..1....1..3..1....2..2..3....3..3..0....1..1..0....0..1..3

R. H. Hardin, Table of n, a(n) for n = 1..53

Empirical: a(n) = (94871989966071037/12399777559663373915599981605027840000000)*n^36 + (23494487319688423/21753995718707673536140318605312000000)*n^35 + (19815461219045083483/196821866026402760565079073095680000000)*n^34 + (387946863583945231/57888784125412576636787962675200000)*n^33 + (1177484665113344641/3432141351309046045659365376000000)*n^32 + (615940986658681/43992616415246567217089740800)*n^31 + (249926773655883881424689/534749765381377174210797895680000000)*n^30 + (4630069145782751496907/356499843587584782807198597120000)*n^29 + (178133742871226319480781/585385621654490612162887680000000)*n^28 + (6962809860198885640273/1147814944420569827770368000000)*n^27 + (666626499383242550268556343/6439241838199396733791764480000000)*n^26 + (522351494242690781724431/343976593920907945181184000000)*n^25 + (259385049672212475250399091383/13522407860218733140962705408000000)*n^24 + (94069937609216051584228677343/450746928673957771365423513600000)*n^23 + (150606744114958980477692573/77125905356322873802752000000)*n^22 + (60407333375536982936116523/3856295267816143690137600000)*n^21 + (18552609924642994134467759158073/173070531619588528813375488000000)*n^20 + (398421495171448567208594349137/641001968961438995605094400000)*n^19 + (32999625284514089244451420058951999/10903443492034077315242655744000000)*n^18 + (3444424661623804094160490174561/281306591641746060764774400000)*n^17 + (813052700533005951081065902821133/19997645460246573707427840000000)*n^16 + (95627195506301062688987740160173/874896988885787599699968000000)*n^15 + (283794291443517721003321123962583391/1207357844662386887585955840000000)*n^14 + (20165452979436273060452527083533/51596489088136191777177600000)*n^13 + (65311515436625900041815166858211147/115247794263227839269568512000000)*n^12 + (2590786840107227108334729278011/10271639417399985674649600000)*n^11 + (330914440339976752306544596432769/198840224746769909022720000000)*n^10 - (36168405113352687550265305231771/2540736205097615504179200000)*n^9 - (4359271111022264447540327478101011/1228022499130514160353280000000)*n^8 - (1695820430249495689620665968078387/5116760413043809001472000000)*n^7 + (7268239430782963931795377473941916839/30534267764838930216284160000000)*n^6 - (139344733258938107220685649337424153/63613057843414437950592000000)*n^5 + (47437635676535991526724411394898871/8239405587337489105981440000)*n^4 - (238200143499847388140289435527/18790835585060867328000)*n^3 + (14071590518507157155692107883/589755662301693888000)*n^2 - (635163845155509650059/16044839210400)*n + 20888560 for n>3

cp's OEIS Frontend

A223795 Number of n X n 0..3 arrays with rows and antidiagonals unimodal.

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A223796 Number of nX3 0..3 arrays with rows and antidiagonals unimodal.

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A223797 Number of nX4 0..3 arrays with rows and antidiagonals unimodal.

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A223798 Number of n X 5 0..3 arrays with rows and antidiagonals unimodal.

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A223799 Number of nX6 0..3 arrays with rows and antidiagonals unimodal.

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A223800 Number of nX7 0..3 arrays with rows and antidiagonals unimodal.

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A223802 Number of 3Xn 0..3 arrays with rows and antidiagonals unimodal.

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A223803 Number of 4Xn 0..3 arrays with rows and antidiagonals unimodal.

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A223804 Number of 5Xn 0..3 arrays with rows and antidiagonals unimodal.

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A223805 Number of 6Xn 0..3 arrays with rows and antidiagonals unimodal.

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