A071726 -id:A071726 - cp's OEIS frontend

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

Wolfdieter Lang, Jan 13 2006

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.

			[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.

W. Lang: First 10 rows.

Row sums give A115128.

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

A115134 Third diagonal sequence of triangle A115127.

Original entry on oeis.org

10, 30, 95, 311, 1043, 3564, 12363, 43420, 154088, 551684, 1990326, 7228417, 26405725, 96961560, 357688755, 1324982160, 4926502020, 18379785300, 68783559810, 258141170430, 971310800694, 3663524817768, 13848466284350

Offset: 4

Wolfdieter Lang, Jan 13 2006

Cf. A071726 (second diagonal of A115127 for n>=3 with g.f. -(1+x+3*x^2)+(1+x^2)*c(x)).

G.f. -(1+x^2+4*x^3) + (1-x+x^3)*c(x) with the g.f. c(x):=(1-sqrt(1-4*x))/(2*x) of A000108 (Catalan).

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cp's OEIS Frontend

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

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