A379435 Number of rooted planar maps with n edges and without faces or vertices of degree 1.

1, 0, 1, 2, 10, 52, 281, 1570, 9022, 53084, 318634, 1945396, 12052532, 75624616, 479814937, 3074251682, 19869323638, 129420288076, 848897059790, 5603350613308, 37198680816844, 248241480270680, 1664546969372554, 11210468046615412, 75806810042727980, 514537522249147672

Offset

0,4

Links

Table of n, a(n) for n=0..25.

Formula

G.f.: 2*x + G(x/(1 + 2*x)^2)*(1 - 2*x)/(1 + 2*x) where G(x) is the g.f. of A000168.

Prog

(PARI) seq(n)={my(z=x/(1 + 2*x)^2, g=(-1 + 18*z + sqrt(1-12*z + O(x^(n+3)))^3) / (54*z^2)); Vec(2*x + g*(1-2*x)/(1+2*x))}

Crossrefs

Cf. A000168, A006396 (sensed), A006397 (unsensed), A379433.

Sequence in context: A344576 A360317 A074612 * A104497 A166694 A238796

Adjacent sequences: A379432 A379433 A379434 * A379436 A379437 A379438

Keyword

nonn

Author

Andrew Howroyd, Jan 14 2025

Status

approved