152020

Appears in sequences

• Sum of lengths of longest increasing subsequences of all permutations of n elements.at n=7A003316
• Number of lattice paths from (0,0) to the line x+y=n that use the step set {(0,1),(1,0),(2,0),(3,0),...} and never pass below y=x.at n=17A089324
• Triangle read by rows: T(n,k) (0 <= k <= floor(n/2)) is the number of Delannoy paths of length n, having k EE's crossing the line y = x (i.e., two consecutive E steps from the line y = x+1 to the line y = x-1).at n=20A110121
• Number of Delannoy paths of length n with no EE's crossing the line y = x (i.e., no two consecutive E steps from the line y = x+1 to the line y = x-1).at n=8A110122
• Define two triangular arrays by: B(0,0)=C(0,0)=1, B(0,r)=C(0,r)=0 for r>0, C(t,-1)=C(t,0); and for t,r >= 0, B(t+1,r)=C(t,r-1)+2C(t,r)-B(t,r), C(t+1,r)=B(t+1,r)+2B(t+1,r+1)-C(t,r). Sequence gives array C(t,r) read by rows.at n=36A177020
• Number of equivalence classes of ballot paths of length n for the string dud.at n=29A274113
• Number of maximal cliques in the n-polygon diagonal intersection graph.at n=41A291949
• Number of primes of the form b^2+1 for b <= 10^n that end in 1.at n=6A301943
• a(n) = 108*n^2 - 104*n + 20 (n>=1).at n=37A304835