A013992 Number of edge-disjoint paths between opposite corners of 3 X n grid.

1, 1, 8, 72, 800, 9754, 121130, 1508919, 18787340, 233941432, 2912502538, 36262251784, 451462592746, 5620827261214, 69979671635586, 871259379376415, 10847277968319460, 135050246142276024, 1681392997487494568, 20933580943579610208, 260625895660539796224

Offset

0,3

References

rec.puzzles Dec 10 1995.

Links

Sean A. Irvine, Table of n, a(n) for n = 0..100

Sean A. Irvine, Note on A013992

Formula

G.f.: (49*x^16 + 49*x^15 - 745*x^14 - 990*x^13 + 4108*x^12 + 10320*x^11 - 994*x^10 - 12122*x^9 + 2071*x^8 + 433*x^7 + 6952*x^6 - 7424*x^5 + 3184*x^4 - 583*x^3 - 5*x^2 + 15*x - 1) / ((7*x^8 - 19*x^7 - 22*x^6 + 98*x^5 + 39*x^4 + 38*x^3 - 60*x^2 + 17*x - 1) * (7*x^8 + 33*x^7 + 38*x^6 - 34*x^5 - 87*x^4 + 94*x^3 - 30*x^2 + x + 1)). - Sean A. Irvine, Sep 18 2018

Mathematica

CoefficientList[Series[(49 x^16 + 49 x^15 - 745 x^14 - 990 x^13 + 4108 x^12 + 10320 x^11 - 994 x^10 - 12122 x^9 + 2071 x^8 + 433 x^7 + 6952 x^6 - 7424 x^5 + 3184 x^4 - 583 x^3 - 5 x^2 + 15 x-1) / ((7 x^8 - 19 x^7 - 22 x^6 + 98 x^5 + 39 x^4 + 38 x^3 - 60 x^2 + 17 x - 1) (7 x^8 + 33 x^7 + 38 x^6 - 34 x^5 - 87 x^4 + 94 x^3 - 30 x^2 + x + 1)), {x, 0, 33}], x] (* Vincenzo Librandi, Sep 18 2018 *)

Crossrefs

Cf. A013990, A013991, A013993, A013994, A013995, A013996, A013997.

Sequence in context: A049388 A014479 A377678 * A279156 A129103 A111812

Adjacent sequences: A013989 A013990 A013991 * A013993 A013994 A013995

Keyword

nonn

Author

Dan Hoey

Status

approved