Bruce Fontaine - cp's OEIS frontend

User: Bruce Fontaine

Bruce Fontaine has authored 2 sequences.

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

Bruce Fontaine, Sep 16 2014

nonn

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

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

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

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

A247415 Number of friezes of type D_n.

Original entry on oeis.org

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

Bruce Fontaine, Sep 16 2014

nonn

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

Cf. A000108, A247416 and A000984, the number of friezes of type A_n, B_n and C_n.

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

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

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

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

cp's OEIS Frontend

User: Bruce Fontaine

A247416 Number of friezes of type B_n.

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