

A167666


Triangle read by rows given by [1,1,4,2,0,0,0,0,0,0,0,...] DELTA [1,0,0,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.


3



1, 1, 1, 2, 3, 1, 0, 4, 5, 1, 0, 0, 6, 7, 1, 0, 0, 0, 8, 9, 1, 0, 0, 0, 0, 10, 11, 1, 0, 0, 0, 0, 0, 12, 13, 1, 0, 0, 0, 0, 0, 0, 14, 15, 1, 0, 0, 0, 0, 0, 0, 0, 16, 17, 1, 0, 0, 0, 0, 0, 0, 0, 0, 18, 19, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 21, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 23, 1, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET

0,4


COMMENTS

Row sums = A111284(n+1), Diagonal sums = A109613(n).


LINKS

Table of n, a(n) for n=0..98.


FORMULA

T(n,k) = 2*T(n1,k1)  T(n2,k2), T(0,0) = T(1,0) = T(1,1) = 1, T(2,0) = 2, T(2,1) = 3, T(3,0) = 0, T(3,1) = 4.  Philippe Deléham, Feb 18 2012
G.f.: (1+(1y)*x+(2+y)*x^2)/(1y*x)^2.  Philippe Deléham, Feb 18 2012
Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A130779(n), A111284(n+1), A167667(n), A167682(n) for x = 1, 0, 1, 2, 3 respectively.  Philippe Deléham, Feb 18 2012


EXAMPLE

Triangle begins :
1 ;
1, 1 ;
2, 3, 1 ;
0, 4, 5, 1 ;
0, 0, 6, 7, 1 ;
0, 0, 0, 8, 9, 1 ;
0, 0, 0, 0, 10, 11, 1 ; ...


CROSSREFS

Cf. A000012, A005408, A005843
Sequence in context: A137396 A244213 A178245 * A115352 A275808 A038554
Adjacent sequences: A167663 A167664 A167665 * A167667 A167668 A167669


KEYWORD

nonn,tabl


AUTHOR

Philippe Deléham, Nov 08 2009


STATUS

approved



