|
| |
|
|
A251970
|
|
Number of (n+1)X(4+1) 0..3 arrays with nondecreasing sum of every two consecutive values in every row and column
|
|
1
|
|
|
|
40000, 1750000, 76562500, 1500625000, 29412250000, 345888060000, 4067643585600, 33470895790080, 275417656786944, 1738925256499200, 10979183698560000, 56483045388000000, 290580293025000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
|
|
|
LINKS
|
|
|
|
FORMULA
|
Empirical for n mod 2 = 0: a(n) = (1/1662081589978752614400)*n^30 + (11/92337866109930700800)*n^29 + (943/83104079498937630720)*n^28 + (47953/69253399582448025600)*n^27 + (351019/11542233263741337600)*n^26 + (1181903/1154223326374133760)*n^25 + (237977021/8656674947806003200)*n^24 + (871812367/1442779157967667200)*n^23 + (23980946683/2164168736951500800)*n^22 + (6888391429/40077198832435200)*n^21 + (410890073857/180347394745958400)*n^20 + (469036933181/18034739474595840)*n^19 + (34778169875659/135260546059468800)*n^18 + (49833698053129/22543424343244800)*n^17 + (560393123760047/33815136514867200)*n^16 + (611489881425653/5635856085811200)*n^15 + (174883489382521/281792804290560)*n^14 + (1091661732017293/352241005363200)*n^13 + (10689328634913073/792542262067200)*n^12 + (1122700571624951/22015062835200)*n^11 + (8262098206990751/49533891379200)*n^10 + (1936285038107993/4127824281600)*n^9 + (14335680552163/12740198400)*n^8 + (340108128733/149299200)*n^7 + (38196515411/9953280)*n^6 + (1215850999/230400)*n^5 + (996397801/172800)*n^4 + (1732123/360)*n^3 + 2877*n^2 + (3290/3)*n + 200
Empirical for n mod 2 = 1: a(n) = (1/1662081589978752614400)*n^30 + (11/92337866109930700800)*n^29 + (755/66483263599150104576)*n^28 + (96137/138506799164896051200)*n^27 + (5643637/184675732219861401600)*n^26 + (95327689/92337866109930700800)*n^25 + (3084026953/110805439331916840960)*n^24 + (14195232967/23084466527482675200)*n^23 + (6285606168799/554027196659584204800)*n^22 + (1818323341547/10259762901103411200)*n^21 + (437381284243303/184675732219861401600)*n^20 + (1259711797335533/46168933054965350400)*n^19 + (150997718345688499/554027196659584204800)*n^18 + (43773380747151701/18467573221986140160)*n^17 + (1994221212754510117/110805439331916840960)*n^16 + (1379281874698406689/11542233263741337600)*n^15 + (128194112142692914747/184675732219861401600)*n^14 + (65109099544047901109/18467573221986140160)*n^13 + (25976938716966335630849/1662081589978752614400)*n^12 + (2783881569199717975213/46168933054965350400)*n^11 + (335060423413374542064199/1662081589978752614400)*n^10 + (160839481936796469771881/277013598329792102400)*n^9 + (87990300630403205261087/61558577406620467200)*n^8 + (4580647671213936778057/1538964435165511680)*n^7 + (4243423147407000686647/820781032088272896)*n^6 + (111714413920756533355/15199648742375424)*n^5 + (28125244339036387375/3377699720527872)*n^4 + (2034213950902854875/281474976710656)*n^3 + (5078568035210551875/1125899906842624)*n^2 + (1014269878926871875/562949953421312)*n + (389325925610015625/1125899906842624)
|
|
|
EXAMPLE
|
Some solutions for n=1
..1..0..2..1..3....0..0..3..3..3....1..1..3..2..3....0..1..3..2..3
..0..1..0..3..1....1..3..1..3..2....0..0..2..3..3....1..0..1..0..1
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
