A219818 Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal, vertical or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 4Xn array

10, 33, 169, 648, 2179, 7049, 22017, 65842, 188487, 519028, 1381594, 3567948, 8961630, 21932971, 52387683, 122289966, 279347375, 625196496, 1372463293, 2958423704, 6267975073, 13064759179, 26813365624, 54226962440, 108144189873

Offset

1,1

Comments

Row 4 of A219816

Links

R. H. Hardin, Table of n, a(n) for n = 1..113

Formula

Empirical: a(n) = (1/2585201673888497664000000)*n^25 - (61/620448401733239439360000)*n^24 + (41/3231502092360622080000)*n^23 - (13501/13488008733331292160000)*n^22 + (103463/2043637686868377600000)*n^21 - (102173/70067577835487232000)*n^20 + (6019/1429117263544320000)*n^19 + (26760289/16133981738434560000)*n^18 - (8215501219/107559878256230400000)*n^17 + (2269026527/1518492398911488000)*n^16 + (15379229167/3479878414172160000)*n^15 - (6289315887821/5965505852866560000)*n^14 + (1889023949230097/69597568283443200000)*n^13 - (3449492823594221/16703416388026368000)*n^12 - (4241521042837721/632705166213120000)*n^11 + (495656982597364909/1898115498639360000)*n^10 - (5695118687610620599/1222271343820800000)*n^9 + (11288184614322257833/230485453406208000)*n^8 - (77413097549306612227/327506039562240000)*n^7 - (6036501181925463108707/4257578514309120000)*n^6 + (1210248151956181009242973/32523169206528000000)*n^5 - (112323084120688445903917/325231692065280000)*n^4 + (344879943990858960613/184699479444480)*n^3 - (126899595321666973457/21202746364800)*n^2 + (33173267893330547/3346393050)*n - 5216328 for n>11

Example

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

Crossrefs

Sequence in context: A004638 A211033 A020479 * A264251 A140866 A219848

Adjacent sequences: A219815 A219816 A219817 * A219819 A219820 A219821

Keyword

nonn

Author

R. H. Hardin Nov 28 2012

Status

approved