A049339 -id:A049339 - cp's OEIS frontend

A049340 Triangle read by rows: T(n,k) is the number of planar graphs with n >= 1 nodes and 0 <= k <= binomial(n,2) edges, all degrees even.

1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 3, 2, 2, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 3, 4, 4, 6, 5, 5, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 3, 4, 7, 9, 15, 17, 22, 14, 16, 5, 4, 0, 1, 0, 0, 0

Offset: 1

Brendan McKay

			Triangle begins:
  1;
  1, 0;
  1, 0, 0, 1;
  1, 0, 0, 1, 1, 0, 0;
  1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0;
  1, 0, 0, 1, 1, 1, 3, 2, 2, 1, 1, 0, 1, 0, 0, 0;
  ...

Sean A. Irvine, Table of n, a(n) for n = 1..231, rows 1..11 flattened
Sean A. Irvine, Java program (github)

Rows sums give A049339.

Cf. A000944, A021103, A003094, A049334.

Entry revised by Sean A. Irvine, Jul 29 2021

A210345 The number of degree sequences of simple graphs with n vertices with all even degrees.

Original entry on oeis.org

1, 1, 2, 3, 7, 14, 36, 74, 201, 425, 1178, 2515, 7063, 15209, 43088, 93382, 266236, 579950, 1661548, 3634062, 10451798, 22935259, 66170288, 145601216, 421164456, 928875440, 2692737120, 5950570725, 17282501978, 38257352346, 111292168834, 246730727752, 718763328317, 1595578916923, 4653944394630

Offset: 1

Tanya Khovanova and Dai Yang, Mar 20 2012

nonn

a(2n) = A210346(n). For even n, the complementary sequence has all odd degrees.

			For n=3, there are only two degree sequences with all even terms are possible: {0,0,0} and {2,2,2}. Thus, a(3)=2.

Cf. A210346, A049339

a(13)-a(35) from Robert Gerbicz, Apr 08 2012

A049365 Number of connected planar graphs with n nodes and even degrees (i.e., that are Eulerian).

Original entry on oeis.org

1, 0, 1, 1, 3, 7, 21, 81, 401, 2499, 18604, 158515, 1464681, 14305475

Offset: 1

Brendan McKay

M. Kirchweger, M. Scheucher, and S. Szeider, SAT-Based Generation of Planar Graphs, in preparation.

Inverse Euler transform of A049339.

a(12) from Sean A. Irvine, Jul 30 2021

a(13)-a(14) from Manfred Scheucher, Mar 11 2023

cp's OEIS Frontend

A049340 Triangle read by rows: T(n,k) is the number of planar graphs with n >= 1 nodes and 0 <= k <= binomial(n,2) edges, all degrees even.

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A210345 The number of degree sequences of simple graphs with n vertices with all even degrees.

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A049365 Number of connected planar graphs with n nodes and even degrees (i.e., that are Eulerian).

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Keywords

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