A238116
Number of continuations arising in matrix method for enumerating Hamiltonian cycles on 2n X 2n grid.
Original entry on oeis.org
1, 14, 162, 1966, 25567, 351880, 5056350, 75100735, 1144833705, 17821104101
Offset: 1
A238117
Number of states with reflective symmetry arising in matrix method for enumerating Hamiltonian cycles on 2n X 2n grid.
Original entry on oeis.org
1, 4, 14, 40, 120, 320, 946, 2496, 7418, 19616
Offset: 1
A238118
Number of continuations with reflective symmetry arising in matrix method for enumerating Hamiltonian cycles on 2n X 2n grid.
Original entry on oeis.org
1, 6, 20, 101, 327, 1560, 5333, 24727, 88422, 403552
Offset: 1
A381676
a(n) = Sum_{k=0..n} binomial(n,k) * ( binomial(n,k) - binomial(n,k-1) )^2.
Original entry on oeis.org
1, 1, 4, 17, 86, 472, 2752, 16753, 105394, 680366, 4484360, 30067160, 204508240, 1408057120, 9796738304, 68786005361, 486845236106, 3470187822754, 24891491746792, 179556655434382, 1301857088258836, 9482632068303296, 69361538748381824, 509303099950899352
Offset: 0
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[ &+[Binomial(n, k)^2 * (Binomial(n, k) - (k gt 0 select Binomial(n, k-1) else 0)) : k in [0..n]] : n in [0..20] ]; // Vincenzo Librandi, Mar 27 2025
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Table[Sum[Binomial[n,k]^2*(Binomial[n,k]-Binomial[n,k-1]),{k,0,n}],{n,0,20}] (* Vincenzo Librandi, Mar 27 2025 *)
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a(n) = sum(k=0, n, binomial(n, k)*(binomial(n, k)-binomial(n, k-1))^2);
Showing 1-4 of 4 results.