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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 (list; table; graph; refs; listen; history; text; internal format)
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, 2012,  arXiv:1212.2732 [math.CO].

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)*A002260(n).

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 * A323474 A132814 A058623

Adjacent sequences:  A187878 A187879 A187880 * A187882 A187883 A187884

KEYWORD

nonn,easy,tabl

AUTHOR

Gary W. Adamson, Mar 14 2011

STATUS

approved

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Last modified September 17 06:41 EDT 2019. Contains 327119 sequences. (Running on oeis4.)