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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
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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 March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)