A225050 Number of shortest paths from one vertex of a cube (side = n units) to farthest vertex, along the grid on 3 surfaces meeting at another vertex.
1, 4, 24, 148, 920, 5754, 36204, 229128, 1458072, 9325030, 59905274, 386368008, 2500651244, 16234450288, 105680341560, 689579733648, 4509096746904, 29539804567230, 193843622021910, 1273932593379600, 8383551165082170, 55238332546851630, 364364231864557080
Offset: 0
Crossrefs
Cf. A060774.
Programs
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Maple
A225050:=n->2*binomial(3*n,n)-binomial(2*n,n); seq(A225050(n), n=0..30); # Wesley Ivan Hurt, May 10 2014
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Mathematica
Table[2*Binomial[3 n, n] - Binomial[2 n, n], {n, 30}] -
PARI
a(n)=2*binomial(3*n,n)-binomial(2*n,n) \\ Charles R Greathouse IV, Apr 26 2013
Formula
a(n) = 2*binomial(3n,n) - binomial(2n,n).