login
A187881
Triangle read by rows: the n-th column consists of n n's followed by 0's.
0
1, 0, 2, 0, 2, 3, 0, 0, 3, 4, 0, 0, 3, 4, 5, 0, 0, 0, 4, 5, 6, 0, 0, 0, 4, 5, 6, 7, 0, 0, 0, 0, 5, 6, 7, 8, 0, 0, 0, 0, 5, 6, 7, 8, 9, 0, 0, 0, 0, 0, 6, 7, 8, 9, 10, 0, 0, 0, 0, 0, 6, 7, 8, 9, 10, 11
OFFSET
1,3
COMMENTS
Row sums = A001318: (1, 2, 5, 7, 12,...)
The triangle is a variant of Janet's periodic table:
.......1
.......2
.....2,3
.....3,4
...3,4,5
...4,5,6
.4,5,6,7
.5,6,7,8
...
FORMULA
As an infinite lower triangular matrix, A * B, where A = A101688 and B = an infinite lower triangular matrix with (1, 2, 3,...) as the main diagonal and the rest zeros.
From Boris Putievskiy, Jan 09 2013: (Start)
a(n) = A101688(n-1)*A002260(n). [Corrected by Georg Fischer, Dec 13 2022]
a(n) = floor((2*A002260(n)+1)/(A003056(n)+3))*A002260(n).
a(n) = floor((2*n-t*(t+1)+1)/(t+3))*(n-t*(t+1)/2), where t = floor((-1+sqrt(8*n-7))/2). (End)
EXAMPLE
First few rows of the triangle:
1
0, 2
0, 2, 3
0, 0, 3, 4
0, 0, 3, 4, 5
0, 0, 0, 4, 5, 6
0, 0, 0, 4, 5, 6, 7
...
CROSSREFS
Sequence in context: A098489 A128064 A144217 * A344839 A344836 A323474
KEYWORD
nonn,easy,tabl
AUTHOR
Gary W. Adamson, Mar 14 2011
STATUS
approved