56400

Appears in sequences

• T(n,k) = right- or upward-moving paths connecting opposite corners of an n X n chessboard, visiting the diagonal at k points between start and finish.at n=31A075435
• Successively larger 3-ball indecomposable ground-state site swaps of A084511 in concatenated decimal notation.at n=34A084512
• Successively larger 3-ball 'prime' ground-state site swaps of A084521 in concatenated decimal notation.at n=28A084522
• a(0)=0, a(1)=1, a(2)=4, a(3)=13; thereafter a(n+3)=4*a(n+2)-4*a(n+1)+2*a(n) for n>=1.at n=11A159036
• Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} having k double descents and initial descents (n>=0; 0<=k<=max(0,n-1)) [we say that i is a doubledescent of a permutation p if p(i) > p(i+1) > p(i+2); we say that a permutation p has an initial descent if p(1) > p(2)].at n=40A162976
• 8-step Fibonacci sequence starting with 0,0,1,0,0,0,0,0.at n=24A251744
• Least positive integer k such that both k and k*n belong to the set {m>0: m+1, m^2+1 and m^2+prime(m)^2 are all prime}.at n=37A261339
• Expansion of Product_{k>=1} 1/(1 - x^k)^(k*(3*k+1)/2).at n=10A294667
• Number of ways to write n as an ordered sum of 10 primes.at n=16A340966
• a(n) = 1*binomial(n,2) + 3*binomial(n,3) + 6*binomial(n,4) + 10*binomial(n,5).at n=16A361474
• Numbers k such that the powerful part of the sum of divisors of k (A387726) is greater than or equal to k, and sigma(k) is not itself a powerful number.at n=40A387729