A307461 Number of longest paths in the stacked book graph S_{n+1} square P_n.

1, 8, 102, 288, 12960, 86400, 7076160, 81285120, 10659962880, 188116992000, 36212520960000, 910486241280000, 242106568704000000, 8225167160770560000, 2889880846678425600000, 127553361508564992000000, 57245948645043968409600000, 3184956415524264424243200000

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Andrew Howroyd, Number of longest paths in the stacked book graph, Feb 2026.

Eric Weisstein's World of Mathematics, Longest Path.

Eric Weisstein's World of Mathematics, Stacked Book Graph.

Formula

From Andrew Howroyd, Feb 13 2026: (Start)

a(n) = n * (n - 1) * ((n/2 - 1)!)^2 * n! for even n >= 4.

a(n) = 3 * (2*n - 1) * (((n-1)/2)!)^2 * n! for odd n >= 5.

a(n) = ((n^2 + 5*n - 3) + (n^2 - 7*n + 3)*(-1)^n) * (floor((n-1)/2)!)^2 * n! / 2 for n >= 4. (End)

Prog

(PARI) a(n) = n!*if(n<4, [1, 4, 17][n], n%2==0, n*(n-1)*(n/2-1)!^2, 3*(2*n-1)*((n-1)/2)!^2); \\ Andrew Howroyd, Feb 13 2026

Crossrefs

Cf. A307028 (longest path lengths).

Sequence in context: A302870 A317862 A318551 * A318213 A001575 A366016

Adjacent sequences: A307458 A307459 A307460 * A307462 A307463 A307464

Keyword

nonn

Author

Eric W. Weisstein, Apr 09 2019

Extensions

a(9) onward from Andrew Howroyd, Feb 13 2026

Status

approved