A222003 Number of nX5 arrays with each row a permutation of 1..5 having at least as many downsteps as the preceding row, with rows in lexicographically nonincreasing order

120, 3853, 78376, 1227685, 16011558, 180224522, 1788225862, 15883318341, 127864299298, 942615276569, 6419292213136, 40684542916124, 241500003506194, 1349966084204199, 7140088927351586, 35880243705890673, 171932038247810370

Offset

1,1

Comments

Column 5 of A222005

Links

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

Formula

Empirical: a(n) = 66*a(n-1) -2145*a(n-2) +45760*a(n-3) -720720*a(n-4) +8936928*a(n-5) -90858768*a(n-6) +778789440*a(n-7) -5743572120*a(n-8) +37014131440*a(n-9) -210980549208*a(n-10) +1074082795968*a(n-11) -4922879481520*a(n-12) +20448884000160*a(n-13) -77413632286320*a(n-14) +268367258592576*a(n-15) -855420636763836*a(n-16) +2515943049305400*a(n-17) -6848956078664700*a(n-18) +17302625882942400*a(n-19) -40661170824914640*a(n-20) +89067326568860640*a(n-21) -182183167981760400*a(n-22) +348524321356411200*a(n-23) -624439409096903400*a(n-24) +1049058207282797712*a(n-25) -1654284096099796392*a(n-26) +2450791253481179840*a(n-27) -3413602103063071920*a(n-28) +4472995859186094240*a(n-29) -5516694892996182896*a(n-30) +6406484391866534976*a(n-31) -7007092303604022630*a(n-32) +7219428434016265740*a(n-33) -7007092303604022630*a(n-34) +6406484391866534976*a(n-35) -5516694892996182896*a(n-36) +4472995859186094240*a(n-37) -3413602103063071920*a(n-38) +2450791253481179840*a(n-39) -1654284096099796392*a(n-40) +1049058207282797712*a(n-41) -624439409096903400*a(n-42) +348524321356411200*a(n-43) -182183167981760400*a(n-44) +89067326568860640*a(n-45) -40661170824914640*a(n-46) +17302625882942400*a(n-47) -6848956078664700*a(n-48) +2515943049305400*a(n-49) -855420636763836*a(n-50) +268367258592576*a(n-51) -77413632286320*a(n-52) +20448884000160*a(n-53) -4922879481520*a(n-54) +1074082795968*a(n-55) -210980549208*a(n-56) +37014131440*a(n-57) -5743572120*a(n-58) +778789440*a(n-59) -90858768*a(n-60) +8936928*a(n-61) -720720*a(n-62) +45760*a(n-63) -2145*a(n-64) +66*a(n-65) -a(n-66)

Example

Some solutions for n=3
..4..2..3..5..1....2..1..3..5..4....4..2..1..3..5....4..2..3..5..1
..3..5..2..4..1....1..4..3..2..5....4..1..2..5..3....3..1..5..2..4
..1..5..4..3..2....1..4..3..2..5....2..1..4..5..3....1..3..2..5..4

Crossrefs

Sequence in context: A052722 A282612 A231136 * A139389 A166596 A000514

Adjacent sequences: A222000 A222001 A222002 * A222004 A222005 A222006

Keyword

nonn

Author

R. H. Hardin Feb 03 2013

Status

approved