A292700 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.)

0, 0, 0, 2, 4, 40, 756, 8466, 70664, 788240, 11086299, 114208465, 1536869680, 19129734630, 228346732944, 3059857239120, 38601632542723, 509554928113867, 6793745301391293, 92409631618813044, 1240139159309482820, 16995549322569645324, 236256012348427662180

Offset

1,4

Links

Table of n, a(n) for n=1..23.

Formula

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)).

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

Example

U, D, L and R express up, down, left and right.
n = 4:
3R, 5U, 7L, 11D, 13L, 17U, 19R, 23U, 29L, 31U, 37R, 41U, 43R, 47D, 53L, 59D.
3R, 5U, 7L, 11U, 13L, 17D, 19R, 23U, 29L, 31U, 37R, 41D, 43R, 47U, 53L, 59D.

Crossrefs

Cf. A000040, A007219, A292698, A292699.

Sequence in context: A238719 A158213 A012596 * A012676 A184245 A103105

Adjacent sequences: A292697 A292698 A292699 * A292701 A292702 A292703

Keyword

nonn

Author

Seiichi Manyama, Sep 21 2017

Status

approved