A223975 -id:A223975 - cp's OEIS frontend

A223970 Number of n X 3 0..2 arrays with rows and antidiagonals unimodal.

22, 484, 9515, 186004, 3628696, 70779056, 1380511272, 26926081924, 525177301935, 10243271456697, 199788923564609, 3896764235253108, 76004070829222317, 1482414237420454682, 28913608801546792225, 563942758255071088641

Offset: 1

R. H. Hardin, Mar 30 2013

nonn

Column 3 of A223975.

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

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

Cf. A223975.

Empirical: a(n) = 22*a(n-1) - 43*a(n-2) - 125*a(n-3) + 283*a(n-4) - 70*a(n-5) - 111*a(n-6) + 45*a(n-7).

Empirical g.f.: x*(22 - 187*x^2 + 236*x^3 + 27*x^4 - 141*x^5 + 45*x^6) / ((1 - x)*(1 - 3*x)*(1 - 18*x - 32*x^2 + 51*x^3 + 17*x^4 - 15*x^5)). - Colin Barker, Aug 25 2018

A223971 Number of nX4 0..2 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

46, 2116, 76092, 2558848, 84988435, 2809740785, 92756321858, 3060966419662, 100999995564503, 3332485315028073, 109953896394879299, 3627869207377692043, 119699463417292189730, 3949414024096794560292, 130308602654739064528903

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Column 4 of A223975

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

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

Empirical: a(n) = 46*a(n-1) -475*a(n-2) +1981*a(n-3) -20047*a(n-4) +170659*a(n-5) -619313*a(n-6) +1472430*a(n-7) -5125985*a(n-8) +14966969*a(n-9) -26289219*a(n-10) +49504177*a(n-11) -100448013*a(n-12) +127366991*a(n-13) -120709682*a(n-14) +121925145*a(n-15) -83316868*a(n-16) +21878656*a(n-17) -230400*a(n-18)

A223972 Number of nX5 0..2 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

86, 7396, 440628, 22935921, 1140963027, 55803232969, 2708281019793, 131014406127439, 6329626912147424, 305632588672082728, 14754359445820013164, 712195518319828970133, 34376429801121343195388

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Column 5 of A223975

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 43

Empirical recurrence of order 43 (see link above)

A223973 Number of nX6 0..2 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

148, 21904, 2026448, 153196498, 10676374380, 715985189481, 47087051658638, 3065213211139220, 198505156112480574, 12821707501426587223, 827061911875686602143, 53312878153050071853965, 3435377864410521923551264

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Column 6 of A223975

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 91

Empirical recurrence of order 91 (see link above)

A223974 Number of nX7 0..2 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

239, 57121, 7829639, 822895397, 76942621022, 6766457318128, 574360426081996, 47758165568891552, 3923597116646870013, 320103299171867245506, 26009282573098001541721, 2108303995165038876541532

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Column 7 of A223975

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

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

A223976 Number of 3Xn 0..2 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

27, 729, 9515, 76092, 440628, 2026448, 7829639, 26375691, 79507149, 218578373, 555979549, 1323191288, 2972776392, 6350443334, 12975277251, 25482263325, 48302292951, 88682057873, 158180868607, 274824912452, 466153399196

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Row 3 of A223975

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

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

Empirical: a(n) = (5051/239500800)*n^12 + (17911/39916800)*n^11 + (132833/21772800)*n^10 + (35869/725760)*n^9 + (2045741/7257600)*n^8 + (425867/403200)*n^7 + (62493899/21772800)*n^6 + (727483/145152)*n^5 + (33993559/5443200)*n^4 + (2107249/907200)*n^3 + (3822521/831600)*n^2 + (49331/13860)*n + 1

A223977 Number of 4Xn 0..2 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

81, 6561, 186004, 2558848, 22935921, 153196498, 822895397, 3731866676, 14772553616, 52279545002, 168389072033, 500454038667, 1387317570171, 3618413260028, 8942729611918, 21066089007345, 47533740360251

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Row 4 of A223975

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

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

Empirical: a(n) = (456419/5230697472000)*n^16 + (35741/12108096000)*n^15 + (4696759/65383718400)*n^14 + (1960073/1779148800)*n^13 + (31966559/2612736000)*n^12 + (461185847/4790016000)*n^11 + (496257731/914457600)*n^10 + (445395499/203212800)*n^9 + (228272848649/36578304000)*n^8 + (5589292243/435456000)*n^7 + (282633985/14370048)*n^6 + (3122820053/239500800)*n^5 - (91030209653/108972864000)*n^4 - (327561926401/4540536000)*n^3 + (185306939/3439800)*n^2 + (13865993/360360)*n + 7

A223978 Number of 5Xn 0..2 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

243, 59049, 3628696, 84988435, 1140963027, 10676374380, 76942621022, 453969579904, 2284206888340, 10088688214569, 39954771229458, 144202872415543, 480339235745630, 1491693619175208, 4354474074592966

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Row 5 of A223975

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

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

Empirical: a(n) = (63370093/405483668029440000)*n^20 + (71859847/9357315416064000)*n^19 + (3840596671/12804747411456000)*n^18 + (16093136419/2134124568576000)*n^17 + (89468187533/627683696640000)*n^16 + (124873595783/62768369664000)*n^15 + (2671089252541/125536739328000)*n^14 + (32125296547501/188305108992000)*n^13 + (302581775150461/289700167680000)*n^12 + (44545336450771/9656672256000)*n^11 + (289473882894181/19313344512000)*n^10 + (311624791382747/9656672256000)*n^9 + (1803023416115741/34871316480000)*n^8 + (43416115518617/724250419200)*n^7 + (2936371270324637/47076277248000)*n^6 - (1561630187307499/2615348736000)*n^5 - (2687139777308839/111152321280000)*n^4 - (285271644066077/77189112000)*n^3 + (4647951175288301/586637251200)*n^2 - (79120764337/15519504)*n + 1710 for n>2

A223979 Number of 6Xn 0..2 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

729, 531441, 70779056, 2809740785, 55803232969, 715985189481, 6766457318128, 50783406166411, 317861952928894, 1716630787916775, 8199247742192030, 35287118527617297, 138825002272586304, 505004840634444527

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Row 6 of A223975

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

R. H. Hardin, Table of n, a(n) for n = 1..144
R. H. Hardin, Empirical polynomial of degree 24

Empirical polynomial of degree 24 (see link above)

A223980 Number of 7Xn 0..2 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

2187, 4782969, 1380511272, 92756321858, 2708281019793, 47087051658638, 574360426081996, 5392250304954708, 41292036231202766, 268318893714852915, 1522088317195862139, 7698392543196415664, 35283079262827759084

Offset: 1

R. H. Hardin Mar 30 2013

nonn

Row 7 of A223975

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

R. H. Hardin, Table of n, a(n) for n = 1..113
R. H. Hardin, Empirical polynomial of degree 28

Empirical polynomial of degree 28 (see link above)

cp's OEIS Frontend

A223970 Number of n X 3 0..2 arrays with rows and antidiagonals unimodal.

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A223971 Number of nX4 0..2 arrays with rows and antidiagonals unimodal.

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A223972 Number of nX5 0..2 arrays with rows and antidiagonals unimodal.

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A223973 Number of nX6 0..2 arrays with rows and antidiagonals unimodal.

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A223974 Number of nX7 0..2 arrays with rows and antidiagonals unimodal.

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A223976 Number of 3Xn 0..2 arrays with rows and antidiagonals unimodal.

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A223977 Number of 4Xn 0..2 arrays with rows and antidiagonals unimodal.

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A223978 Number of 5Xn 0..2 arrays with rows and antidiagonals unimodal.

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A223979 Number of 6Xn 0..2 arrays with rows and antidiagonals unimodal.

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A223980 Number of 7Xn 0..2 arrays with rows and antidiagonals unimodal.

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