A292700 - OEIS

%I #41 Sep 27 2017 09:17:16

%S 0,0,0,2,4,40,756,8466,70664,788240,11086299,114208465,1536869680,

%T 19129734630,228346732944,3059857239120,38601632542723,

%U 509554928113867,6793745301391293,92409631618813044,1240139159309482820,16995549322569645324,236256012348427662180

%N 1/4 of the number of paths that are made of alternate vertical and horizontal 4*n consecutive prime (> 2 and < prime(4*n+2)) steps. (Each path begins and ends at the same point but is allowed to intersect itself.)

%F Constant term in the expansion of (1/4) * Product_{k=1..2*n} (x^prime(2*k) + 1/x^prime(2*k)) * Product_{k=1..2*n} (y^prime(2*k+1) + 1/y^prime(2*k+1)).

%F a(n) = A292698(n) * A292699(n).

%e U, D, L and R express up, down, left and right.

%e n = 4:

%e 3R, 5U, 7L, 11D, 13L, 17U, 19R, 23U, 29L, 31U, 37R, 41U, 43R, 47D, 53L, 59D.

%e 3R, 5U, 7L, 11U, 13L, 17D, 19R, 23U, 29L, 31U, 37R, 41D, 43R, 47U, 53L, 59D.

%Y Cf. A000040, A007219, A292698, A292699.

%K nonn

%O 1,4

%A _Seiichi Manyama_, Sep 21 2017