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 A166124 Triangle, read by rows, given by [0,1/2,1/2,0,0,0,0,0,0,0,...] DELTA [2,-1,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. 0
 1, 0, 2, 0, 1, 2, 0, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..104. FORMULA Sum_{k, 0<=k<=n} T(n,k)*x^(n-k)= A166122(n), A166114(n), A084222(n), A084247(n), A000034(n), A040000(n), A000027(n+1), A000079(n), A007051(n), A047849(n), A047850(n), A047851(n), A047852(n), A047853(n), A047854(n), A047855(n), A047856(n) for x= -5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,11 respectively. Sum_{k, 0<=k<=n} T(n,k)*x^k= A000007(n), A000027(n+1), A033484(n), A134931(n), A083597(n) for x= 0,1,2,3,4 respectively. T(n,k)= A166065(n,k)/2^(n-k). G.f.: (1-x+x*y)/(1-x-x*y+x^2*y). - Philippe Deléham, Nov 09 2013 T(n,k) = T(n-1,k) + T(n-1,k-1) - T(n-2,k-1), T(0,0) = 1, T(1,0) = 0, T(1,1) = 2, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Nov 09 2013 EXAMPLE Triangle begins : 1 ; 0,2 ; 0,1,2 ; 0,1,1,2 ; 0,1,1,1,2 ; 0,1,1,1,1,2 ; 0,1,1,1,1,1,2 ; ... CROSSREFS Sequence in context: A299196 A227698 A331466 * A134979 A112248 A244860 Adjacent sequences: A166121 A166122 A166123 * A166125 A166126 A166127 KEYWORD nonn,tabl AUTHOR Philippe Deléham, Oct 07 2009 STATUS approved

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Last modified May 23 22:02 EDT 2024. Contains 372765 sequences. (Running on oeis4.)