27744

Appears in sequences

• Expansion of 1/((1+x)*(1-x)^5).at n=31A001752
• Coordination sequence for D_4 lattice.at n=12A007900
• Numbers k such that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 83.at n=39A031581
• Number of nondividing sets on {1,2,...,n}.at n=41A051014
• a(n) = n^2*(n^2 - 1)/3.at n=17A112742
• Sum of divisors of 2^n + 3^n.at n=8A114705
• a(n) = 4*n*(floor(n^2/2)+1). For n >= 3, this is the number of directed Hamiltonian paths on the n-prism graph.at n=24A124350
• Number of (directed) Hamiltonian paths in the n-Möbius ladder graph.at n=21A137883
• a(n) = (prime(n)^4 - prime(n)^2)/3.at n=6A138419
• Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 1), (0, 0, 1), (1, -1, 1), (1, 1, -1)}.at n=10A148385
• Number of 2-step self-avoiding walks on an n X n X n cube summed over all starting positions.at n=16A187163
• E.g.f.: exp( Sum_{n>=1} x^(2*n)/A000108(n) ) = Sum_{n>=0} a(n)*x^(2*n)/(2*n)!, where A000108 is the Catalan numbers.at n=4A193442
• a(n) = 24*n^2.at n=34A195824
• Number of n X 4 0..3 arrays with no element equal to another at a city block distance of exactly two, and new values 0..3 introduced in row major order.at n=7A222834
• Number of 3-cycles in the n X n black bishop graph.at n=24A289161
• a(n) = 27*n^2 - 51*n + 24, n>=1.at n=32A304836
• Numbers k such that 301*2^k+1 is prime.at n=13A322915
• Numbers k of the earliest occurrence of widths patterns in the symmetric representation of sigma listed in the ordering of patterns in A342595.at n=29A342596
• Indices of 0 in A348295: numbers m such that Sum_{k=1..m} (-1)^(floor(k*(sqrt(2)-1))) = Sum_{k=1..m} (-1)^A097508(k) = 0.at n=34A348299
• a(n) = (2*n^4 - 6*(-1)^n*n^2 - 2*n^2 + 3*(-1)^n - 3)/96.at n=34A350050