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A206474
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Riordan array ((1+x-x^2)/(1-x^2), x/(1-x^2)).
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1
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1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 2, 1, 1, 1, 1, 3, 3, 1, 1, 0, 3, 3, 4, 4, 1, 1, 1, 1, 6, 6, 5, 5, 1, 1, 0, 4, 4, 10, 10, 6, 6, 1, 1, 1, 1, 10, 10, 15, 15, 7, 7, 1, 1, 0, 5, 5, 20, 20, 21, 21, 8, 8, 1, 1, 1, 1, 15, 15, 35, 35, 28, 28, 9, 9, 1, 1
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OFFSET
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0,12
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COMMENTS
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Triangle T(n,k), read by rows, given by (1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
Antidiagonal sums are A158780(n+1).
Row sums are 2*Fibonacci(n) = 2*A000045(n), n>0.
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LINKS
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Table of n, a(n) for n=0..77.
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FORMULA
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T(2n, 2k) = A128908(n,k), T(2n+1, 2k) = T(2n+1, 2k+1) = A085478(n,k) = Binomial (n+k, 2k), T(2n+2, 2k+1) = A078812(n,k) = Binomial(n+k-1, 2k-1).
T(n,k) = T(n-1,k-1) + T(n-2,k), T(0,0) = T(0,1) = 1, T(0,2) = 0.
G.f.: (1+x-x^2)/(1-x*y-x^2).
Sum_{k, 0<=k<=n} T(n,k)*x^k = (-1)^n* A000129(n) (n>0), A000007(n), A135528(n-1), A055389(n) for x = -2, -1, 0, 1 respectively .
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EXAMPLE
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Triangle begins :
1
1, 1
0, 1, 1
1, 1, 1, 1
0, 2, 2, 1, 1
1, 1, 3, 3, 1, 1
0, 3, 3, 4, 4, 1, 1
1, 1, 6, 6, 5, 5, 1, 1
0, 4, 4, 10, 10, 6, 6, 1, 1
1, 1, 10, 10, 15, 15, 7, 7, 1, 1
0, 5, 5, 20, 20, 21, 21, 8, 8, 1, 1
1, 1, 15, 15, 35, 35, 28, 28, 9, 9, 1, 1
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CROSSREFS
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Cf. A007318, A078812, A085478, A128908,
Sequence in context: A165031 A099245 A185331 * A211999 A175025 A076899
Adjacent sequences: A206471 A206472 A206473 * A206475 A206476 A206477
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Philippe Deléham, Feb 08 2012
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STATUS
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approved
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