A309117 Number of perfect matchings on a triangular lattice of width 4 and length n.
1, 1, 5, 15, 56, 203, 749, 2777, 10293, 38240, 141997, 527593, 1960029, 7282483, 27057400, 100531559, 373522965, 1387822193, 5156442953, 19158736256, 71184183353, 264484479633, 982690786037, 3651182836279, 13565952140920, 50404229548515, 187276671274621
Offset: 0
Links
- S. N. Perepechko, Number of perfect matchings on triangular lattices of fixed width, DIMA'2015 slides.
Formula
G.f.: (1-z)*(1+z)*(1-z-5*z^2-z^3+z^4)/((1+z-3*z^2-3*z^3+z^4)*(1-3*z-3*z^2+z^3+z^4)).