OFFSET
0,2
COMMENTS
Number of n X n binary symmetric matrices with rows, considered as binary numbers, in nondecreasing order. - R. H. Hardin, May 30 2008
Also, number of (n+1) X (n+1) binary symmetric matrices with zero main diagonal and rows, considered as binary numbers, in nondecreasing order. - Max Alekseyev, Feb 06 2022
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..50
FORMULA
a(n) = Sum_{k=0..n} A097712(n, k). - Paul D. Hanna, Aug 24 2004
Equals the binomial transform of A008934 (number of tournament sequences): a(n) = Sum_{k=0..n} C(n, k)*A008934(k). - Paul D. Hanna, Sep 18 2005
MATHEMATICA
T[n_, k_] := T[n, k] = If[n < 0 || k > n, 0, If[n == k, 1, If[k == 0, 1, T[n - 1, k] + Sum[T[n - 1, j] T[j, k - 1], {j, 0, n - 1}]]]];
a[n_] := Sum[T[n, k], {k, 0, n}];
a /@ Range[0, 20] (* Jean-François Alcover, Oct 02 2019 *)
PROG
(SageMath)
@CachedFunction
def T(n, k): # T = A097712
if k<0 or k>n: return 0
elif k==0 or k==n: return 1
else: return T(n-1, k) + sum(T(n-1, j)*T(j, k-1) for j in range(n))
def A016121(n): return sum(T(n, k) for k in range(n+1))
[A016121(n) for n in range(31)] # G. C. Greubel, Feb 21 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved