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A336667
Triangular array read by rows. T(n,k) is the number of closed walks of length 2n along the edges of a cube based at vertex v that return to v exactly k times, n>=0, 0<=k<=n.
0
1, 0, 3, 0, 12, 9, 0, 84, 72, 27, 0, 588, 648, 324, 81, 0, 4116, 5544, 3564, 1296, 243, 0, 28812, 45864, 35748, 16848, 4860, 729, 0, 201684, 370440, 337932, 193104, 72900, 17496, 2187
OFFSET
0,3
LINKS
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; page 340.
FORMULA
O.g.f.: (1 - 7*x^2)/(1 - 7*x^2 - 3*y*x^2 + 9*y*x^4).
EXAMPLE
Triangle T(n,k) begins:
1;
0, 3;
0, 12, 9;
0, 84, 72, 27;
0, 588, 648, 324, 81;
...
MATHEMATICA
Table[nn = n; CoefficientList[Series[(1 - 7 z^2)/(1 - (7 + 3 u) z^2 + 9 u z^4), {z, 0, nn}], {z, u}][[-1]], {n, 0, 15, 2}] // Grid
CROSSREFS
Cf. A054879 (row sums), A328778 (column k=1).
Sequence in context: A110890 A249010 A071534 * A269880 A135687 A057374
KEYWORD
nonn,tabl,easy
AUTHOR
Geoffrey Critzer, Jul 29 2020
STATUS
approved