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A166124

Triangle, read by rows, given by [0,1/2,1/2,0,0,0,0,0,0,0,...] DELTA [2,-1,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.
(history; published version)

#8 by N. J. A. Sloane at Sat Nov 09 14:16:09 EST 2013

STATUS

proposed

approved

#7 by Michel Marcus at Sat Nov 09 13:03:19 EST 2013

STATUS

editing

proposed

#6 by Michel Marcus at Sat Nov 09 13:03:04 EST 2013

FORMULA

Sum_{k, 0<=k<=n} T(n,k)*x^(n-k)= A166122(n), A166114(n), A084222(n), A084247(n), A000034(n), A040000(n), A000027(n+1), A000079(n), A007051(n), A047849(n), A047850(n), A047851(n), A047852(n), A047853(n), A047854(n), A047855(n), A047856(n) for x= -5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11 respectively. Sum_{k, 0<=k<=n} T(n,k)*x^k= A000007(n), A000027(n+1), A033484(n), A134931(n), A083597(n) for x= 0,1,2,3,4 respectively. T(n,k)= A166065(n,k)/2^(n-k).

Sum_{k, 0<=k<=n} T(n,k)*x^k= A000007(n), A000027(n+1), A033484(n), A134931(n), A083597(n) for x= 0,1,2,3,4 respectively.

T(n,k)= A166065(n,k)/2^(n-k).

G.f.: (1-x+x*y)/(1-x-x*y+x^2*y). - Philippe Deléham , , Nov 09 2013

T(n,k) = T(n-1,k) + T(n-1,k-1) - T(n-2,k-1), T(0,0) = 1, T(1,0) = 0, T(1,1) = 2, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham , , Nov 09 2013

EXAMPLE

Triangle begins : 1 ; 0,2 ; 0,1,2 ; 0,1,1,2 ; 0,1,1,1,2 ; 0,1,1,1,1,2 ; 0,1,1,1,1,1,2 ; ...

Triangle begins :

1 ;

0,2 ;

0,1,2 ;

0,1,1,2 ;

0,1,1,1,2 ;

0,1,1,1,1,2 ;

0,1,1,1,1,1,2 ; ...

STATUS

proposed

editing

#5 by Philippe Deléham at Sat Nov 09 10:22:32 EST 2013

STATUS

editing

proposed

#4 by Philippe Deléham at Sat Nov 09 10:22:21 EST 2013

FORMULA

G.f.: (1-x+x*y)/(1-x-x*y+x^2*y). - Philippe Deléham , Nov 09 2013

T(n,k) = T(n-1,k) + T(n-1,k-1) - T(n-2,k-1), T(0,0) = 1, T(1,0) = 0, T(1,1) = 2, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham , Nov 09 2013

STATUS

approved

editing

#3 by N. J. A. Sloane at Sun Sep 08 13:31:48 EDT 2013

AUTHOR

_Philippe DELEHAM_, Deléham_, Oct 07 2009

Discussion

Sun Sep 08

13:31

OEIS Server: https://oeis.org/edit/global/1938

#2 by Russ Cox at Sat Mar 31 10:28:09 EDT 2012

AUTHOR

_Philippe DELEHAM (kolotoko(AT)wanadoo.fr), _, Oct 07 2009

Discussion

Sat Mar 31

10:28

OEIS Server: https://oeis.org/edit/global/535

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

Triangle, read by rows, given by [0,1/2,1/2,0,0,0,0,0,0,0,...] DELTA [2,-1,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.

DATA

1, 0, 2, 0, 1, 2, 0, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2

OFFSET

0,3

FORMULA

EXAMPLE

Triangle begins : 1 ; 0,2 ; 0,1,2 ; 0,1,1,2 ; 0,1,1,1,2 ; 0,1,1,1,1,2 ; 0,1,1,1,1,1,2 ; ...

KEYWORD

nonn,tabl

AUTHOR

Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 07 2009

STATUS

approved