A096037 Triangle T(n,m) = (3*n+3*m-2)*(n+1-m)/2 read by rows.

2, 7, 5, 15, 13, 8, 26, 24, 19, 11, 40, 38, 33, 25, 14, 57, 55, 50, 42, 31, 17, 77, 75, 70, 62, 51, 37, 20, 100, 98, 93, 85, 74, 60, 43, 23, 126, 124, 119, 111, 100, 86, 69, 49, 26, 155, 153, 148, 140, 129, 115, 98, 78, 55, 29, 187, 185, 180, 172, 161, 147, 130, 110, 87, 61, 32

Offset

1,1

Links

Table of n, a(n) for n=1..66.

Formula

T(n,m) = (3*n+3*m-2)*(n+1-m)/2 .

T(n,m) = A094930(n,m)/(3*m-1).

T(n,1) = A005449(n).

T(n,n) = A016768(n-1).

Row sums: sum_{m=1..n} T(n,m) = n^2*(n+1) = A011379(n).

Example

The triangle starts in row n=1 as
2;
7,5;
15,13,8;
26,24,19,11;

Prog

(Python)
def A096037(n, m):
    return (3*n+3*m-2)*(n+1-m)//2
print( [A096037(n, m) for n in range(20) for m in range(1, n+1)] )
# R. J. Mathar, Oct 11 2009

Crossrefs

Cf. A094930, A024212, A011379, A002411, A096038, A095794.

Sequence in context: A165355 A038004 A100792 * A286379 A343314 A233248

Adjacent sequences: A096034 A096035 A096036 * A096038 A096039 A096040

Keyword

nonn,easy,tabl

Author

Gary W. Adamson, Jun 17 2004

Extensions

Edited and extended, A-numbers corrected by R. J. Mathar, Oct 11 2009

Status

approved