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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..35.

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

Adjacent sequences: A336664 A336665 A336666 * A336668 A336669 A336670

KEYWORD

nonn,tabl,easy

AUTHOR

Geoffrey Critzer, Jul 29 2020

STATUS

approved

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Last modified December 1 18:36 EST 2022. Contains 358475 sequences. (Running on oeis4.)