44576

Appears in sequences

• Triangular array T: put T(n,0)=n for all n >= 0 and all other T(n,k)=0; then put T(n,k)=Sum{T(i,j): 0<=j<=i-n+k, n-k<=i<=n}.at n=44A054144
• Number of routes of length 2n on the sides of an octagon from a point to opposite point.at n=9A060995
• Number of n step walks (each step +/-1 starting from 0) which are never more than 3 or less than -3.at n=17A068912
• A126988^12 * A000594.at n=7A128392
• Number of binary strings of length n with equal numbers of 00010 and 00100 substrings.at n=16A164211
• The sum of the entries in the top rows of all 2-compositions of n. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.at n=8A181292
• Number of (n+1) X 5 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.at n=14A202331
• a(n) is the first occurrence of n in sequence A209266.at n=30A211389
• T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, without move-in move-out left turns.at n=29A221655
• Number of 2Xn arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, without move-in move-out left turns.at n=6A221656
• G.f.: -log(1-x) = Sum_{n>=1} a(n) * [ Sum_{k>=1} k^n * x^k ]^n / n.at n=4A276745
• Number of n-element subsets of [2n] whose sum is a triangular number.at n=11A284251
• a(n) = Sum_{d|n} max(d, n/d)^4.at n=11A297843
• Wiener index of the graph of nodes (i,j) of the square lattice such that abs(i) + abs(j) <= n.at n=7A302298
• Number of unlabeled leafless loopless multigraphs with n edges.at n=12A307316
• a(n) = Sum_{k=1..n} phi(k) * (floor(n/k)^4 - floor((n-1)/k)^4).at n=21A344600
• Triangular array read by rows. T(n,k) is the number of partial permutations on [n] with exactly k connected components, n>=0, 0<=k<=n.at n=42A350227
• Numbers k for which A354102(k) = A354102(sigma(k)).at n=28A354106
• G.f. A(x) satisfies A(x) = (1 + x)^3 * B(x*A(x)), where B(x) is the g.f. of A001764.at n=6A381939