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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Alternatively, a(n) = k if n+1 is the k-th 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*y-1)^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

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Last modified December 16 01:32 EST 2019. Contains 330013 sequences. (Running on oeis4.)