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A152815 Triangle T(n,k), read by rows given by [1,0,-1,0,0,0,0,0,0,...] DELTA [0,1,-1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. 15
1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 1, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 0, 0, 0, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,12

COMMENTS

Triangle read by rows, Pascal's triangle (A007318) rows repeated.

Riordan array (1/(1-x), x^2/(1-x^2)). - Philippe Deléham, Feb 27 2012

LINKS

Reinhard Zumkeller, Rows n = 0..150 of triangle, flattened

FORMULA

T(n,k) = T(n-1,k) + ((1+(-1)^n)/2)*T(n-1,k-1).

G.f.: (1+x)/(1-(1+y)*x^2).

Sum_{k=0..n} T(n,k)*x^k = A000012(n), A016116(n), A108411(n), A213173(n), A074872(n+1) for x = 0,1,2,3,4 respectively. - Philippe Deléham, Nov 26 2011, Apr 22 2013

EXAMPLE

Triangle begins:

  1;

  1, 0;

  1, 1, 0;

  1, 1, 0, 0;

  1, 2, 1, 0, 0;

  1, 2, 1, 0, 0, 0;

  1, 3, 3, 1, 0, 0, 0;

  1, 3, 3, 1, 0, 0, 0, 0;

  1, 4, 6, 4, 1, 0, 0, 0, 0; ...

MATHEMATICA

m = 13;

(* DELTA is defined in A084938 *)

DELTA[Join[{1, 0, -1}, Table[0, {m}]], Join[{0, 1, -1}, Table[0, {m}]], m] // Flatten (* Jean-François Alcover, Feb 19 2020 *)

PROG

(Haskell)

a152815 n k = a152815_tabl !! n !! k

a152815_row n = a152815_tabl !! n

a152815_tabl = [1] : [1, 0] : t [1, 0] where

   t ys = zs : zs' : t zs' where

     zs' = zs ++ [0]; zs = zipWith (+) ([0] ++ ys) (ys ++ [0])

-- Reinhard Zumkeller, Feb 28 2012

CROSSREFS

Cf. A007318, A064861, A152198 (another version), A000931 (diagonal sums), A016116 (row sums).

Sequence in context: A288969 A305355 A218380 * A115296 A059048 A257181

Adjacent sequences:  A152812 A152813 A152814 * A152816 A152817 A152818

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Dec 13 2008

EXTENSIONS

Example corrected by Philippe Deléham, Dec 13 2008

STATUS

approved

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Last modified May 10 04:12 EDT 2021. Contains 343748 sequences. (Running on oeis4.)