A187881 Triangle read by rows: the n-th column consists of n n's followed by 0's.

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

...

Links

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

Boris Putievskiy, Transformations (of) Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

Wikipedia, Electron configuration

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

Cf. A001318, A101688.

Sequence in context: A098489 A128064 A144217 * A344839 A344836 A323474

Adjacent sequences: A187878 A187879 A187880 * A187882 A187883 A187884

Keyword

nonn,easy,tabl

Author

Gary W. Adamson, Mar 14 2011

Status

approved