A248971 Triangular array read by rows. T(n,k)=C(k,2)+C(n-k,2),n>=2,1<=k<=floor(n/2).

0, 1, 3, 2, 6, 4, 10, 7, 6, 15, 11, 9, 21, 16, 13, 12, 28, 22, 18, 16, 36, 29, 24, 21, 20, 45, 37, 31, 27, 25, 55, 46, 39, 34, 31, 30, 66, 56, 48, 42, 38, 36, 78, 67, 58, 51, 46, 43, 42, 91, 79, 69, 61, 55, 51, 49, 105, 92, 81, 72, 65, 60, 57, 56

Offset: 2

Author

Geoffrey Critzer, Oct 18 2014

Keywords

• nonn
• tabf

Comments

G is a simple graph of order n with exactly 2 components each of which is complete. T(n,k) is the total number of edges in G when one component contains exactly k vertices.

Examples

			0,
1,
3, 2,
6, 4,
10, 7,  6,
15, 11, 9,
21, 16, 13, 12,
28, 22, 18, 16,
36, 29, 24, 21, 20
		

Crossrefs

Cf. A000217 (column 1), A000124 (column 2), A152950 (column 3), A002620 (row ends).

Programs

Magma

[Binomial(k,2)+Binomial(n-k,2): k in [1..Floor(n/2)], n in [1..16]]; // Vincenzo Librandi, Oct 19 2014

Mathematica

Table[Table[Binomial[k, 2] + Binomial[n - k, 2], {k, 1, n/2}], {n, 2,
   10}] // Grid