A247415 Number of friezes of type D_n.

1, 4, 14, 51, 187, 695, 2606, 9842, 37386, 142693, 546790, 2102312, 8106308, 31335060, 121390028, 471159761, 1831860961, 7133082300, 27813493104, 108585087657, 424396534100, 1660418620528, 6502345229958, 25485677806201, 99969379431223, 392424954930562, 1541494622610616, 6059022365002926, 23829761312067896

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, A247416 and A000984, the number of friezes of type A_n, B_n and C_n.

Programs

Maple

a:= n -> add(numtheory:-tau(m)*binomial(2*n-m-1,n-m),m=1..n):
seq(a(n),n=1..100); # Robert Israel, Sep 17 2014

Mathematica

a[n_] := Sum[DivisorSigma[0, m] Binomial[2n-m-1, n m], {m, 1, n}]
Array[a, 29] (* Jean-François Alcover, Sep 18 2018 *)

PARI

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

Formula

a(n) = sum_{m=1..n} A000005(m)*binomial(2n-m-1,n-m).