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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 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 (Python) for i in range(1, 15):     print(i, end=", ")     for j in range(i):         print("0", end=", ") # Mohammad Saleh Dinparvar, May 11 2020 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 April 10 15:47 EDT 2021. Contains 342845 sequences. (Running on oeis4.)