A247416 Number of friezes of type B_n.

2, 6, 21, 75, 273, 1008, 3762, 14158, 53635, 204270, 781378, 2999906, 11553234, 44612760, 172671925, 669679793, 2601913466, 10125418060, 39459828905, 153977743500, 601545298200, 2352559491900, 9209476821105, 36084150102001, 141499349638556, 555292275455022, 2180689496523468, 8569380062230708

Offset: 1

Author

Bruce Fontaine, Sep 16 2014

Keywords

• nonn

Links

• B. Fontaine and P.-G. Plamondon, Counting friezes in type D_n, arXiv:1409.3698 [math.CO], 2014.

Crossrefs

Cf. A000108, A000984 and A247415, the number of friezes of type A_n, C_n and D_n.

Programs

PARI

a(n) = sum(m=1,sqrtint(n+1), binomial(2*n-m^2+1,n) ); \\ Joerg Arndt, Sep 16 2014

Formula

a(n) = sum_{m=1..floor(sqrt(n+1))} binomial(2n-m^2+1,n).