

A127648


Triangle read by rows: row n consists of n zeros followed by n+1.


40



1, 0, 2, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15
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OFFSET

0,3


COMMENTS

Alternatively, a(n) = k if n+1 is the kth triangular number and 0 otherwise.
Triangle T(n,k), 0<=k<=n, read by rows, given by (0,0,0,0,0,0,0,0,0,0,...) DELTA (2,1/2,1/2,0,0,0,0,0,0,0,...)where DELTA is the operator defined in A084938.  Philippe Deléham, Oct 27 2011


LINKS

Table of n, a(n) for n=0..119.


FORMULA

Infinite lower triangular matrix with (1, 2, 3,...) in the main diagonal and the rest zeros.
This sequence * A007318 (Pascal's Triangle) = A003506.
A007318 * this sequence = A103406.
G.f.: 1/(x*y1)^2.  R. J. Mathar, Aug 11 2015
a(n) = (1/2) (Round(Sqrt(4 + 2 n))  Round(Sqrt(2 + 2 n))) (1 + Round(Sqrt(2 + 2 n)) + Round(Sqrt(4 + 2 n))).  Brian Tenneson, Jan 27 2017


EXAMPLE

First few rows of the triangle are:
1;
0, 2;
0, 0, 3;
0, 0, 0, 4;
0, 0, 0, 0, 5;
0, 0, 0, 0, 0, 6;
0, 0, 0, 0, 0, 0, 7;
...


MAPLE

A127648 := proc(n)
for i from 0 do
if A000217(i) = n+1 then
return i ;
elif A000217(i) >n then
return 0 ;
end if;
end do;
end proc: # R. J. Mathar, Apr 23 2013


MATHEMATICA

Flatten[Table[{n, Table[0, {n}]}, {n, 15}]] (* Harvey P. Dale, Jul 27 2011 *)


PROG

(Haskell)
a127648 n k = a127648_tabl !! n !! k
a127648_row n = a127648_tabl !! n
a127648_tabl = map reverse $ iterate (\(x:xs) > x + 1 : 0 : xs) [1]
a127648_list = concat a127648_tabl
 Reinhard Zumkeller, Jul 13 2013


CROSSREFS

Cf. A007318, A003506, A103406, A084938.
Cf. A010054.
Sequence in context: A284269 A140579 A132681 * A212209 A259481 A132825
Adjacent sequences: A127645 A127646 A127647 * A127649 A127650 A127651


KEYWORD

nonn,easy,tabl


AUTHOR

Gary W. Adamson, Jan 22 2007


STATUS

approved



