login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A039735 Triangle read by rows: T(n,k) = number of nonisomorphic unlabeled planar graphs with n >= 1 nodes and 0<=k<=3n-6 edges. 5
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 1, 1, 1, 2, 4, 6, 6, 6, 4, 2, 1, 1, 1, 2, 5, 9, 15, 21, 24, 24, 20, 13, 5, 2, 1, 1, 2, 5, 10, 21, 41, 65, 97, 130, 144, 135, 98, 51, 16, 5, 1, 1, 2, 5, 11, 24, 56, 115, 221, 401, 658, 956, 1217, 1264, 1042, 631, 275, 72, 14, 1, 1, 2, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

Planar graphs with n >= 3 nodes have at most 3n-6 edges. - Charles R Greathouse IV, Feb 18 2013

REFERENCES

R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.

R. J. Wilson, Introduction to Graph Theory. Academic Press, NY, 1972, p. 162.

LINKS

Table of n, a(n) for n=1..76.

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

Sum_{k} T(n, k) = A005470(n) if n>=1. - Michael Somos, Aug 23 2015

log(1 + A(x, y)) = Sum{n>0} B(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 A049334. - Michael Somos, Aug 23 2015

EXAMPLE

Triangle starts

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

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

1:  1

2:  1  1

3:  1  1  1  1

4:  1  1  2  3  2  1  1

5:  1  1  2  4  6  6  6  4  2  1

6:  1  1  2  5  9 15 21 24 24 20 13  5  2

CROSSREFS

Cf. A005470 (row sums), A008406, A049334.

Sequence in context: A255252 A174985 A008406 * A283761 A171457 A129385

Adjacent sequences:  A039732 A039733 A039734 * A039736 A039737 A039738

KEYWORD

nonn,tabf,nice

AUTHOR

Brendan McKay

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 17 19:36 EDT 2018. Contains 316293 sequences. (Running on oeis4.)