A227668 Number of lattice paths from {n}^6 to {0}^6 using steps that decrement one component by 1 such that for each point (p_1,p_2,...,p_6) we have abs(p_{i}-p_{i+1}) <= 1.

1, 720, 1413792, 2940381648, 6173789662504, 12981179566917088, 27297846037161958056, 57403822541579269311072, 120712076511505386344017520, 253839841305922000782983605664, 533787802709908480895773030991840, 1122477022599575074944649300433060288

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

G.f.: -(67322341490688000*x^20 +27865599006421811200*x^19 -8662296440668699099136*x^18 -16874516373657444974592*x^17 +27085359075023950995456*x^16 -1808862947855651445760*x^15 -1414381090428803492096*x^14 -3613053959743748878592*x^13

+1363837434430612756288*x^12 +93587353840530417152*x^11 -39568432789577322400*x^10 -4418148372274485344*x^9 +81199402070343168*x^8 +9376560118889840*x^7 -221663818632940*x^6 +2817001053384*x^5 -695598308*x^4 +124162308*x^3 -958790*x^2 +2064*x -1)

/ ( -13254524928000000*x^21 -271933737533440000*x^20 -5733118008692572160*x^19 +116739247952003395584000*x^18 +224369280219612051439616*x^17 -356501961858517247606784*x^16 +60501369697833888177152*x^15 +16382732593079984754944*x^14

+13383960686857306419456*x^13 -5739755254392736710336*x^12 -404736183389439184896*x^11 +144333130922005891104*x^10 +16946456787615943968*x^9 -22388465914256448*x^8 -24650905650633712*x^7 +544278444686228*x^6 -5641861520584*x^5 -1907901380*x^4 -244171188*x^3 +1549478*x^2 -2784*x +1).

Example

a(1) = 6! = 720.

Crossrefs

Column k=6 of A227655.

Cf. A000142.

Sequence in context: A221621 A054779 A030185 * A010799 A283830 A075754

Adjacent sequences: A227665 A227666 A227667 * A227669 A227670 A227671

Keyword

nonn,easy

Author

Alois P. Heinz, Jul 19 2013

Status

approved