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A049334 Triangle read by rows: T(n, k) = number of unlabeled connected planar simple graphs with n >= 1 nodes and 0<=k<=3*n-6 edges. 5
1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 2, 2, 1, 1, 0, 0, 0, 0, 3, 5, 5, 4, 2, 1, 0, 0, 0, 0, 0, 6, 13, 19, 22, 19, 13, 5, 2, 0, 0, 0, 0, 0, 0, 11, 33, 67, 107, 130, 130, 96, 51, 16, 5, 0, 0, 0, 0, 0, 0, 0, 23, 89, 236, 486, 804, 1112, 1211, 1026, 626, 275, 72, 14, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,11

COMMENTS

Planar graphs with n >= 3 nodes have at most 3*n-6 edges.

LINKS

Table of n, a(n) for n=1..80.

F. Harary, The number of linear, directed, rooted, and connected graphs, Trans. Amer. Math. Soc. 78 (1955), 445-463. (MR0068198) See page 457, equation (2.9).

FORMULA

T(n, n-1) = A000055(n) and Sum_{k} T(n, k) = A003094(n) if n>=1. - Michael Somos, Aug 23 2015

log(1 + B(x, y)) = Sum{n>0} A(x^n, y^n) / n where A(x, y) = Sum_{n>0, k>=0} T(n,k) * x^n * y^k and similarly B(x, y) with A039735. - Michael Somos, Aug 23 2015

EXAMPLE

n\k 0  1  2  3  4  5  6  7  8  9 10 11 12

--:-- -- -- -- -- -- -- -- -- -- -- -- --

1:  1

2:  0  1

3:  0  0  1  1

4:  0  0  0  2  2  1  1

5:  0  0  0  0  3  5  5  4  2  1

6:  0  0  0  0  0  6 13 19 22 19 13  5  2

CROSSREFS

Cf. A000055, A003094, A039735.

Sequence in context: A083747 A326787 A246271 * A054924 A046751 A124478

Adjacent sequences:  A049331 A049332 A049333 * A049335 A049336 A049337

KEYWORD

nonn,tabf,easy,nice

AUTHOR

Brendan McKay

STATUS

approved

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Last modified December 7 03:00 EST 2019. Contains 329836 sequences. (Running on oeis4.)