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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<=k<=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. - From 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 ; ...

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: A268389 A288969 A218380 * A115296 A059048 A257181

Adjacent sequences:  A152812 A152813 A152814 * A152816 A152817 A152818

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Dec 13 2008

EXTENSIONS

Corrected example. Philippe Deléham, Dec 13 2008

STATUS

approved

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Last modified February 23 23:15 EST 2018. Contains 299595 sequences. (Running on oeis4.)