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A096367
Number of winning paths of length n+1 across an n X n Hex board.
1
2, 14, 58, 194, 578, 1602, 4226, 10754, 26626, 64514, 153602, 360450, 835586, 1916930, 4358146, 9830402, 22020098, 49020930, 108527618, 239075330, 524288002, 1145044994, 2491416578, 5402263554, 11676942338, 25165824002, 54089744386, 115964116994, 248034361346
OFFSET
3,1
COMMENTS
If m>n-2, H(m,n) = (2*m+1-n)*2^(n-2) is the number of winning paths of length n across an m X n Hex board (cf. A001792). If m>n-1, H'(m,n) = (n-2)*(H(m-3,n-2) + H(m+1,n-2)) - 2^(n-1) + 2 is the number of winning paths of length n+1 across an m X n Hex board.
FORMULA
a(n) = (n-2)*(n+1)*2^(n-3)-2^(n-1)+2.
G.f.: -2*x^3*(2*x^2-1) / ((x-1)*(2*x-1)^3). - Colin Barker, Sep 06 2013
EXAMPLE
a(4)=14.
PROG
(Python)
def a(n): return (n-2)*(n+1)*2**(n-3) - 2**(n-1) + 2
print([a(n) for n in range(3, 32)]) # Michael S. Branicky, Feb 14 2021
CROSSREFS
Cf. A001792.
Sequence in context: A212895 A115027 A114146 * A232601 A285153 A232370
KEYWORD
nonn,easy
AUTHOR
David Bevan, Jul 02 2004
EXTENSIONS
More terms from Colin Barker, Sep 06 2013
STATUS
approved