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A209599
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Triangle T(n,k), read by rows, given by (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
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0
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1, 2, 0, 3, 1, 0, 5, 3, 0, 0, 8, 7, 1, 0, 0, 13, 15, 4, 0, 0, 0, 21, 30, 12, 1, 0, 0, 0, 34, 58, 31, 5, 0, 0, 0, 0, 55, 109, 73, 18, 1, 0, 0, 0, 0, 89, 201, 162, 54, 6, 0, 0, 0, 0, 0, 144, 365, 344, 145, 25, 1, 0, 0, 0, 0, 0
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refs;
listen;
history;
text;
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OFFSET
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0,2
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COMMENTS
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A skew version of A122075.
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LINKS
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Table of n, a(n) for n=0..65.
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FORMULA
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G.f.: (1+x)/(1-x-(1+y)*x^2).
T(n,k) = T(n-1,k) + T(n-2,k) + T(n-2,k-1), T(0,0) = 1, T(1,0) = 2, T(1,1) = 0, T(n,k) = 0 if k<0 or if k>n.
Sum_{k, 0<=k<=n} T(n,k)*x^k = A040000(n), A000045(n+2), A000079(n), A006138(n), A026597(n), A133407(n), A133467(n), A133469(n), A133479(n), A133558(n), A133577(n), A063092(n) for x = -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 respectively.
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EXAMPLE
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Triangle begins :
1
2, 0
3, 1, 0
5, 3, 0, 0
8, 7, 1, 0, 0
13, 15, 4, 0, 0, 0
21, 30, 12, 1, 0, 0, 0
34, 58, 31, 5, 0, 0, 0, 0
55, 109, 73, 18, 1, 0, 0, 0, 0
89, 201, 162, 54, 6, 0, 0, 0, 0, 0
144, 365, 344, 145, 25, 1, 0, 0, 0, 0, 0
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CROSSREFS
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Cf. A122075, A122950, A000045, A023610, A129707
Sequence in context: A225624 A168020 A225084 * A170942 A002187 A124756
Adjacent sequences: A209596 A209597 A209598 * A209600 A209601 A209602
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Philippe Deléham, Mar 10 2012
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STATUS
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approved
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