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

1,2

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;

Links

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

Formula

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

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

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

Prog

(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

Crossrefs

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

Sequence in context: A213038 A337512 A131828 * A064462 A248266 A325689

Adjacent sequences: A096035 A096036 A096037 * A096039 A096040 A096041

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, Jun 17 2004

Extensions

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

Status

approved