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 A122950 Triangle T(n,k), 0<=k<=n, read by rows, given by [0, 0, 1, -1, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, -1, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. 18
 1, 0, 1, 0, 0, 2, 0, 0, 1, 3, 0, 0, 0, 3, 5, 0, 0, 0, 1, 7, 8, 0, 0, 0, 0, 4, 15, 13, 0, 0, 0, 0, 1, 12, 30, 21, 0, 0, 0, 0, 0, 5, 31, 58, 34, 0, 0, 0, 0, 0, 1, 18, 73, 109, 55, 0, 0, 0, 0, 0, 0, 6, 54, 162, 201, 89, 0, 0, 0, 0, 0, 0, 1, 25, 145, 344, 365, 144, 0, 0, 0, 0, 0, 0, 0, 7, 85, 361, 707 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Skew triangle associated with the Fibonacci numbers. LINKS FORMULA Sum_{k, 0<=k<=n}T(n,k)=A011782(n) . Sum_{n,n>=k}T(n,k)=A001333(k) . T(n,k)=0 if k<0 or if k>n, T(0,0)=1, T(2,1)=0, T(n,k)=T(n-1,k-1)+T(n-2,k-1)+T(n-2,k-2) . T(n,n)=Fibonacci(n+1)=A000045(n+1). Sum_{k, 0<=k<=n}T(n,k)*x^k = A000007(n), A011782(n), A133592(n), A133594(n), A133642(n), A133646(n), A133678(n), A133679(n), A133680(n), A133681(n) for x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 respectively . - Philippe DELEHAM, Jan 03 2008 G.f.: (1-y*x^2)/(1-y*x-y*(y+1)*x^2). - From Philippe DelĂ©ham, Nov 26 2011 EXAMPLE Triangle begins: .1; .0, 1; .0, 0, 2; .0, 0, 1, 3; .0, 0, 0, 3, 5; .0, 0, 0, 1, 7, 8; .0, 0, 0, 0, 4, 15, 13; .0, 0, 0, 0, 1, 12, 30, 21; .0, 0, 0, 0, 0, 5, 31, 58, 34; .0, 0, 0, 0, 0, 1, 18, 73, 109, 55; .0, 0, 0, 0, 0, 0, 6, 54, 162, 201, 89; .0, 0, 0, 0, 0, 0, 1, 25, 145, 344, 365, 144; .0, 0, 0, 0, 0, 0, 0, 7, 85, 361, 707, 655, 233; CROSSREFS Cf. A055830 (another version). Sequence in context: A051510 A153036 A182114 * A116489 A166373 A202451 Adjacent sequences:  A122947 A122948 A122949 * A122951 A122952 A122953 KEYWORD nonn,tabl AUTHOR Philippe DELEHAM, Oct 25 2006 STATUS approved

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