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

2,3

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.

Links

Table of n, a(n) for n=2..65.

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A249742 A246276 A091018 * A329435 A160795 A258212

Adjacent sequences: A248968 A248969 A248970 * A248972 A248973 A248974

Keyword

nonn,tabf

Author

Geoffrey Critzer, Oct 18 2014

Status

approved