A223869 Number of 6Xn 0..3 arrays with rows and antidiagonals unimodal and columns nondecreasing.
84, 7056, 303560, 8008548, 145947740, 1989679315, 21476594002, 191485393983, 1457018264594, 9708014658466, 57822416245144, 313064200874351, 1561981122439360, 7262269235529104, 31752205659432881, 131516275822916936
Offset: 1
Keywords
Examples
Some solutions for n=3 ..0..0..0....0..0..0....0..0..0....0..0..0....0..2..1....0..2..3....0..0..0 ..2..0..0....0..2..1....1..2..0....1..2..0....0..2..1....0..2..3....0..0..0 ..2..3..1....2..3..2....1..2..1....2..2..1....0..2..2....0..3..3....1..0..0 ..2..3..1....3..3..2....1..3..1....2..2..1....0..2..2....1..3..3....1..2..0 ..2..3..1....3..3..2....1..3..2....2..2..1....3..2..2....2..3..3....1..2..0 ..3..3..2....3..3..3....2..3..2....3..2..1....3..3..3....2..3..3....3..2..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = (1/48569119454267387884339200000000)*n^36 + (1/385469202017995141939200000000)*n^35 + (509/2294879094136521281765376000000)*n^34 + (45072673/3373472268380686284195102720000000)*n^33 + (98970929/155735580571551568517529600000000)*n^32 + (15657172481/622942322286206274070118400000000)*n^31 + (72553007/84245463642710408822784000000)*n^30 + (9224227575469/353670479749588078181744640000000)*n^29 + (259388109101239/365866013534056632601804800000000)*n^28 + (1069067947427789/60977668922342772100300800000000)*n^27 + (324068662301467/813035585631236961337344000000)*n^26 + (1050857599757983/125082397789421070974976000000)*n^25 + (3359228653373591/20330730290850174074880000000)*n^24 + (59499006518000473/19544124654597042339840000000)*n^23 + (328837729476779/6275036678399050383360000)*n^22 + (15779074497679499/19015262661815304192000000)*n^21 + (2751358950432231398341/235662488588764336619520000000)*n^20 + (50435698940805547445789/353493732883146504929280000000)*n^19 + (441377463056670747803689/296934735621843064140595200000)*n^18 + (1873830568342196532829127/141397493153258601971712000000)*n^17 + (267354503696336902783274977/2651202996623598786969600000000)*n^16 + (436422377507839553846644063/662800749155899696742400000000)*n^15 + (1125875946010062345791103079/304888344611713860501504000000)*n^14 + (2092746936332381279309322059/117264747927582254039040000000)*n^13 + (751942966419486002702371387/10125656687825770291200000000)*n^12 + (1974716117993688153795059/7436126973898022400000000)*n^11 + (1788367830018388939084527979/2198714023642167263232000000)*n^10 + (31107899679091365256605057767/14658093490947781754880000000)*n^9 + (211320747100198509737825012033/45147885997445373542400000000)*n^8 + (552453635986071137589553754293/63959505163047612518400000000)*n^7 + (32067365980652302617534655703/2434949582523040687104000000)*n^6 + (2243604186621342688240182563/137690601392671943616000000)*n^5 + (21949153806567016754942281/1376906013926719436160000)*n^4 + (391289317973804357849579/32783476522064748480000)*n^3 + (3883508589248023/569647119000960)*n^2 + (22960563482143/10314539492400)*n + 1
Comments