A166065 - OEIS

A166065

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

1, 0, 2, 0, 2, 2, 0, 4, 2, 2, 0, 8, 4, 2, 2, 0, 16, 8, 4, 2, 2, 0, 32, 16, 8, 4, 2, 2, 0, 64, 32, 16, 8, 4, 2, 2, 0, 128, 64, 32, 16, 8, 4, 2, 2, 0, 256, 128, 64, 32, 16, 8, 4, 2, 2, 0, 512, 256, 128, 64, 32, 16, 8, 4, 2, 2, 0, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 2, 0, 2048, 1024

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..80.

FORMULA

Sum_{k, 0<=k<=n} T(n,k)*x^k = (-1)^n*A084247(n), A000007(n), A000079(n), A001787(n+1), A166060(n), A165665(n), A083585(n) for x= -1, 0, 1, 2, 3, 4, 5 respectively. Sum_{k, 0<=k<=n} T(n,k)*x^(n-k) = A040000(n), A000079(n), A095121(n), A047851(n), A047853(n), A047855(n) for x = 0, 1, 2, 3, 4, 5 respectively.

G.f.: (1-2*x+x*y)/((-1+2*x)*(x*y-1)). - R. J. Mathar, Aug 11 2015

EXAMPLE

Triangle begins :

0,2,

0,2,2,

0,4,2,2,

0,8,4,2,2,

0,16,8,4,2,2,

0,32,16,8,4,2,2,

0,64,32,16,8,4,2,2,

0,128,64,32,16,8,4,2,2,

0,256,128,64,32,16,8,4,2,2,

0,512,256,128,64,32,16,8,4,2,2,

CROSSREFS

Sequence in context: A214258 A369279 A138021 * A252706 A139137 A138231

Adjacent sequences: A166062 A166063 A166064 * A166066 A166067 A166068

KEYWORD

nonn,tabl,easy

AUTHOR

Philippe Deléham, Oct 05 2009

STATUS

approved