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

Author

Gary W. Adamson, Jun 17 2004

Keywords

• nonn
• easy
• tabl

Examples

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

Crossrefs

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

Programs

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

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).

Extensions

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