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A223870 Number of 7Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%I A223870 #6 Jul 23 2025 04:36:55
%S A223870 120,14400,857696,30627033,740441932,13140481520,181330154458,
%T A223870 2031375254570,19103100564953,154879319818086,1106319655331310,
%U A223870 7088499061347994,41355557480132029,222496813189773094
%N A223870 Number of 7Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.
%C A223870 Row 7 of A223864
%H A223870 R. H. Hardin, <a href="/A223870/b223870.txt">Table of n, a(n) for n = 1..210</a>
%F A223870 Empirical: a(n) = (1/731743016283032599871082788290560000000)*n^42 + (1/4977843648183895237218250260480000000)*n^41 + (928393/46001848566932971411483888975872000000000)*n^40 + (105277/73145796479098389325092394893312000000)*n^39 + (1194875887417/14630003285779052077202999275526553600000000)*n^38 + (2989034162869/770000172935739583010684172396134400000000)*n^37 + (253954581560803/1578153507593520316530906749730816000000000)*n^36 + (5354203220243/901802004339154466589089571274752000000)*n^35 + (294541461227512613/1487973307159604869871997792603340800000000)*n^34 + (3283448634973867/543651190047352893632443475558400000000)*n^33 + (1695440335227801901/9946345636093615440320840859648000000000)*n^32 + (3573106388063476091/795707650887489235225667268771840000000)*n^31 + (199763950144059168991/1796759211681427305348280929484800000000)*n^30 + (74264834838952433551/28519987487006782624575887769600000000)*n^29 + (22508587327587010087/388203096465609563855388672000000000)*n^28 + (6487713317681801287/5268470594890415509465989120000000)*n^27 + (5879724305315631273143/236027482651090614824076312576000000)*n^26 + (2274008762771343921151/4777884264192117708989399040000000)*n^25 + (1433958075984913204598868559/170382339038756037576130088140800000000)*n^24 + (171994077476794008378711763/1298151154580998381532419719168000000)*n^23 + (4807317857591109327659320591/2616826438088178555658237378560000000)*n^22 + (1168312336634046874744823561/53404621185473031748127293440000000)*n^21 + (3267005930489620041151124845704799/14294414418056675360283121680384000000000)*n^20 + (6168875562195824331118939779649/3009350403801405339006972985344000000)*n^19 + (1421349779115626568528007952265121/87772720110874322387703378739200000000)*n^18 + (443650330465794505186411456583/4008618930894881365898035200000000)*n^17 + (231458296026946241960005215879167/345743382789683517808705536000000000)*n^16 + (2781803526486270651769956719311/790270589233562326419898368000000)*n^15 + (180518342530030480992731139435779501/11029213910990904218097706598400000000)*n^14 + (112422850223626902402310801373206057/1696802140152446802784262553600000000)*n^13 + (256455030218680186741984545055085811457/1087881553947739188785091969024000000000)*n^12 + (10923760852985777320434335065266037/15015618411977076449759723520000000)*n^11 + (88612710087482886643695234551735533/45442003088877994519009689600000000)*n^10 + (5132272050632981323250919168852481/1142060924191378169128550400000000)*n^9 + (176762144080638309567478939777189963/19986066173349117959749632000000000)*n^8 + (12877453273843085031374115529301/876581849708294647357440000000)*n^7 + (93032030615999750514907250146925549/4583262987565425332123834880000000)*n^6 + (60616255337563316970152218520251/2645462041884805386507264000000)*n^5 + (94214291470099334061118441477637/4572870100972306453819699200000)*n^4 + (66435080638421714121718489/4652899980639302456064000)*n^3 + (385110153135599654276494759/50995582363565168801472000)*n^2 + (169896669668551379/73020063246530400)*n + 1
%e A223870 Some solutions for n=3
%e A223870 ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A223870 ..0..0..0....0..0..0....0..0..0....0..0..2....0..0..0....0..2..0....0..0..0
%e A223870 ..0..0..1....0..0..1....0..0..3....1..2..3....2..0..0....0..2..1....0..0..1
%e A223870 ..1..1..2....0..0..2....0..1..3....1..3..3....2..0..0....1..2..1....2..3..1
%e A223870 ..2..2..2....0..2..3....0..1..3....1..3..3....3..1..0....3..2..2....3..3..1
%e A223870 ..3..2..2....1..2..3....1..1..3....1..3..3....3..1..0....3..2..2....3..3..1
%e A223870 ..3..3..2....2..3..3....1..3..3....3..3..3....3..3..2....3..2..2....3..3..3
%K A223870 nonn
%O A223870 1,1
%A A223870 _R. H. Hardin_ Mar 28 2013