A096038 Triangle T(n,m) = (3*n^2-3*m^2+5*m-4+n)/2 read by rows.

1, 6, 4, 14, 12, 7, 25, 23, 18, 10, 39, 37, 32, 24, 13, 56, 54, 49, 41, 30, 16, 76, 74, 69, 61, 50, 36, 19, 99, 97, 92, 84, 73, 59, 42, 22, 125, 123, 118, 110, 99, 85, 68, 48, 25, 154, 152, 147, 139, 128, 114, 97, 77, 54, 28, 186, 184, 179, 171, 160, 146, 129, 109, 86, 60, 31

Offset: 1

Author

Gary W. Adamson, Jun 17 2004

Keywords

• nonn
• tabl
• easy

Comments

The triangle is obtained by subtracting the triangle A094930 from

its square root (also described in A094930) and then dividing each element of column m through 3*m-1.

For the first three rows n=1 to 3 this yields for example:

4;.................2;............2......................1;

14,25;......minus..2,5;.......=..12,20;......->.divide..6,4;

30,65,64;..........2,5,8;........28,60,56;..............14;12,7;

Crossrefs

Cf. A095794, A011379, A002411, A096037, A096036, A024212.

Programs

Python

def A096038(n,m):
    return (3*n**2-3*m**2+5*m-4+n)//2
print( [A096038(n,m) for n in range(20) for m in range(1,n+1)] )
# R. J. Mathar, Oct 11 2009

Formula

T(n,1) = A095794(n).

T(n,n) = 3*n-2.

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

Extensions

Edited, T(3,2) corrected, and extended by R. J. Mathar, Oct 11 2009