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A123110 Triangle T(n,k), 0<=k<=n, read by rows given by [0,1,0,0,0,0,0,0,0,0,...] DELTA [1,0,-1,1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. 5
1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Essentially the same sequence as A114607.

Also essentially the same as A023532. - R. J. Mathar, Jun 18 2008

Diagonal sums give A123108. [From Philippe Deléham, Oct 08 2009]

LINKS

Table of n, a(n) for n=0..104.

FORMULA

Sum {k,0<=k<=n} T(n,k)*x^k = A000007(n),A028310(n),A095121(n),A123109(n) for x=0,1,2,3 respectively.

G.f.: (1-x+y*x^2)/(1-(1+y)*x+y*x^2). - From Philippe Deléham, Nov 01 2011

From Tom Copeland, Nov 10 2012: (Start)

O.g.f. for row polynomials: 1+[t/(1-t)][1/(1-x)-1/(1-x*t)] = 1+t*x+(t+t^2)x^2+....

E.g.f. for row polynomials: 1+[t/(1-t)][e^x-e^(t*x)] = 1+t*x+(t+t^2)x^2/2+.... (End)

EXAMPLE

Triangle begins:

1;

0, 1;

0, 1, 1;

0, 1, 1, 1;

0, 1, 1, 1, 1;

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

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

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

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

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

CROSSREFS

Sequence in context: A213061 A110247 A114607 * A004593 A094934 A245837

Adjacent sequences:  A123107 A123108 A123109 * A123111 A123112 A123113

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Sep 28 2006

STATUS

approved

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Last modified October 21 14:20 EDT 2019. Contains 328301 sequences. (Running on oeis4.)