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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.) 2
0, 0, 0, 2, 4, 40, 756, 8466, 70664, 788240, 11086299, 114208465, 1536869680, 19129734630, 228346732944, 3059857239120, 38601632542723, 509554928113867, 6793745301391293, 92409631618813044, 1240139159309482820, 16995549322569645324, 236256012348427662180 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 22 07:34 EDT 2020. Contains 337289 sequences. (Running on oeis4.)