

A202389


Triangle T(n,k), read by rows, given by (1, 2, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.


1



1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 1, 2, 5, 3, 5, 1, 3, 5, 10, 5, 8, 1, 3, 9, 10, 20, 8, 13, 1, 4, 9, 22, 20, 38, 13, 21, 1, 4, 14, 22, 51, 38, 71, 21, 34, 1, 5, 14, 40, 51, 111, 71, 130, 34, 55
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OFFSET

0,6


COMMENTS

T(n,n) = A000045(n+1) = Fibonacci(n+1).


LINKS

Table of n, a(n) for n=0..54.


FORMULA

T(n,k) = T(n1,k1) + T(n2,k2)  T(n2,k) with T(0,0) = T(1,0) = T(1,1) = 1 and T(n,k) = 0 if k<0 or if n<k.
G.f.: (1+x)/(1y*x+(1y^2)*x^2).
Sum_{k, 0<=k<=n} T(n,k)*x^k = (1)^n*A046717(n), A000007(n), A057077(n), A040000(n), A000244(n) for x = 2, 1, 0, 1, 2 respectively.


EXAMPLE

Triangle begins :
1
1, 1
1, 1, 2
1, 2, 2, 3
1, 2, 5, 3, 5
1, 3, 5, 10, 5, 8
1, 3, 9, 10, 20, 8, 13


CROSSREFS

Cf. A124137, A123585
Sequence in context: A086421 A290399 A109400 * A210868 A176853 A261787
Adjacent sequences: A202386 A202387 A202388 * A202390 A202391 A202392


KEYWORD

sign,tabl


AUTHOR

Philippe Deléham, Dec 18 2011


STATUS

approved



