A143814 Triangle T(n,m) read along rows: T(n,m) = n^2 - (m+1)^2 for 1<=m<n-1, T(n,n-1) = n^2-1.

3, 5, 8, 12, 7, 15, 21, 16, 9, 24, 32, 27, 20, 11, 35, 45, 40, 33, 24, 13, 48, 60, 55, 48, 39, 28, 15, 63, 77, 72, 65, 56, 45, 32, 17, 80, 96, 91, 84, 75, 64, 51, 36, 19, 99, 117, 112, 105, 96, 85, 72, 57, 40, 21, 120, 140, 135, 128, 119, 108, 95, 80, 63, 44, 23, 143

Offset

2,1

Comments

The triangle appears taking the entries of A140978,

4;

9,9;

16,16,16;

25,25,25,25;

..

minus the entries of A133819 with the 1's moved to the end of the rows,

1;

4,1;

4,9,1;

4,9,16,1;

4,9,16,25,1;

The result T(n,m) is a variant of A120070, the first term in each row of A120070 transferred to the end of the row.

Links

Table of n, a(n) for n=2..67.

Example

3;
5,8;
12,7,15;
21,16,9,24;
32,27,20,11,35;

Maple

A143814 := proc(n, m) if m<n-1 then n^2-(m+1)^2 ; elif m=n-1 then n^2-1 ; end if; end proc:
seq(seq(A143814(n, m), m=1..n-1), n=2..14) ; # R. J. Mathar, Jan 23 2011

Crossrefs

Cf. A016061 (row sums).

Sequence in context: A136684 A215751 A115888 * A088971 A153400 A289076

Adjacent sequences: A143811 A143812 A143813 * A143815 A143816 A143817

Keyword

nonn,easy,tabl

Author

Paul Curtz, Sep 02 2008

Status

approved