A115265 Correlation triangle for floor((n+3)/3).

1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 3, 3, 2, 2, 4, 4, 4, 4, 2, 3, 4, 5, 7, 5, 4, 3, 3, 5, 6, 8, 8, 6, 5, 3, 3, 6, 7, 9, 11, 9, 7, 6, 3, 4, 6, 8, 12, 12, 12, 12, 8, 6, 4, 4, 7, 9, 13, 15, 15, 15, 13, 9, 7, 4

Offset

0,5

Comments

Row sums are A115266. Diagonal sums are A115267.

T(2n,n) is A092353. T(2n,n)-T(2n,n+1)=A087508(n+1).

Links

Table of n, a(n) for n=0..65.

Formula

G.f.: (1+x+x^2)(1+xy+x^2*y^2)/((1-x^3)^2*(1-x^3*y^3)^2*(1-x^2*y)).

T(n, k) = sum{j=0..n, [j<=k]*floor((k-j+3)/3)*[j<=n-k]*floor((n-k-j+3)/3)}.

Example

Triangle begins
1;
1,1;
1,2,1;
2,2,2,2;
2,3,3,3,2;
2,4,4,4,4,2;
3,4,5,7,5,4,3;
3,5,6,8,8,6,5,3;
3,6,7,9,11,9,7,6,3;

Mathematica

T[n_, k_] := Sum[Boole[j <= k] * Floor[(k - j + 3)/3] * Boole[j <= n-k] * Floor[(n - k - j + 3)/3], {j, 0, n}]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 15 2017 *)

Crossrefs

Sequence in context: A024937 A350823 A143977 * A105223 A025859 A031281

Adjacent sequences: A115262 A115263 A115264 * A115266 A115267 A115268

Keyword

easy,nonn,tabl

Author

Paul Barry, Jan 18 2006

Status

approved