A115127 Second (k=2) triangle of numbers related to totally asymmetric exclusion process (case alpha=1, beta=1).

3, 6, 7, 10, 16, 19, 15, 30, 47, 56, 21, 50, 95, 146, 174, 28, 77, 170, 311, 471, 561, 36, 112, 280, 586, 1043, 1562, 1859, 45, 156, 434, 1015, 2044, 3564, 5291, 6292, 55, 210, 642, 1652, 3682, 7204, 12363, 18226, 21658, 66, 275, 915, 2562, 6230, 13392, 25623

Offset

2,1

Comments

This is the second floor (k=2) of a pyramid of numbers, called X(1,1,k=2,n,m) with n>=m+1>=2. One could use offset n>=1 and add a zero main diagonal.

The column sequences give for n>=m+1 and m=1..7: A000217, A005581, A024191, A115129, A115130, A115132, A115133.

The diagonal sequences give for M:=n-m=1..3: A071716, A071726, A115134.

Links

Table of n, a(n) for n=2..53.

W. Lang: First 10 rows.

Formula

a(n,m)= b(n,m) + b(n-1,m) with b(n,m):=A115126(n,m) if n=m+1 (main diagonal), A115126(n,m) + a(n,-1,m) if n>m+1 (subdiagonals) and 0 if n<m+1.

Example

[3];[6,7];[10,16,19];[15,30,47,56];...
Main diagonal (n-m=1) example: a(3,2)= 7 = 5 + 2 because
A115126(3,2)=5 and A115126(2,2)=2.
Subdiagonal (n-m>1) example: a(4,2)= 16 = 9 + 7 because
A115126(4,2)=9 and a(3,2)=7.

Crossrefs

Row sums give A115128.

Sequence in context: A024412 A255508 A262972 * A258354 A164557 A292608

Adjacent sequences: A115124 A115125 A115126 * A115128 A115129 A115130

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Jan 13 2006

Status

approved