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 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 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 STATUS approved

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Last modified January 23 22:26 EST 2019. Contains 319404 sequences. (Running on oeis4.)