A342284 Number of friendly 3-watermelons of length n.

1, 0, 2, 6, 24, 110, 550, 2922, 16242, 93520, 553980, 3359384, 20777588, 130696662, 834244830, 5393850898, 35272830054, 233016356788, 1553427829684, 10441803227652, 70715551631992, 482201548554776, 3308810614160224, 22836540660981088, 158458108961055864

Offset

0,3

References

Essam, J.W. and Guttmann, A.J., 1995. Vicious walkers and directed polymer networks in general dimensions. Physical Review E, 52(6), pp. 5849ff. See (63).

Iwan Jensen, Three friendly walkers, Journal of Physics A: Mathematical and Theoretical, Volume 50:2 (2017), #24003, 14 pages; https://doi.org/10.1088/1751-8121/50/2/024003. See F_3(x).

Links

Table of n, a(n) for n=0..24.

Formula

G.f. = 1 - 2*x + G(x), where G(x) = 2*x+2*x^2+6*x^3+24*x^4+110*x^5+550*x^6+... is the g.f. for A342282.

Crossrefs

Cf. A001181, A342282.

Sequence in context: A372527 A138020 A046646 * A174195 A274378 A177521

Adjacent sequences: A342281 A342282 A342283 * A342285 A342286 A342287

Keyword

nonn

Author

N. J. A. Sloane, Mar 19 2021

Status

approved