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A115390
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Binomial transform of tribonacci sequence A000073.
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6
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0, 0, 1, 4, 12, 34, 96, 272, 772, 2192, 6224, 17672, 50176, 142464, 404496, 1148480, 3260864, 9258528, 26287616, 74638080, 211918912, 601698560, 1708394752, 4850622592, 13772308480, 39103533056, 111026143488, 315235058688
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OFFSET
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0,4
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COMMENTS
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See also A117189 Binomial transform of the tribonacci sequence A000073.
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LINKS
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FORMULA
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a(n) = SUM[k=0..n] C(n,k)*A000073(k).
O.g.f.: -x^2/(-1+4*x-4*x^2+2*x^3). - R. J. Mathar, Apr 02 2008
a(n) = sum(sum(binomial(j-1,k-1)*2^(j-k)*binomial(n-j+k-1,2*k-1),j,k,n-k),k,1,n). - Vladimir Kruchinin, Aug 18 2010
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EXAMPLE
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1*0 = 0.
1*0 + 1*0 = 0.
1*0 + 2*0 + 1*1 = 1.
1*0 + 3*0 + 3*1 + 1* 1 = 4.
1*0 + 4*0 + 6*1 + 4*1 + 1*2 = 12.
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MATHEMATICA
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b[0]=b[1]=0; b[2]=1; b[n_]:=b[n]=b[n-1]+b[n-2]+b[n-3]; a[n_]:=Sum[n!/(k!*(n-k)!)*b[k], {k, 0, n}]; Table[a[n], {n, 0, 27}] (* Farideh Firoozbakht, Mar 11 2006 *)
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PROG
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(Maxima) sum(sum(binomial(j-1, k-1)*2^(j-k)*binomial(n-j+k-1, 2*k-1), j, k, n-k), k, 1, n); \\ Vladimir Kruchinin, Aug 18 2010
(Haskell)
a115390 n = a115390_list !! n
a115390_list = 0 : 0 : 1 : map (* 2) (zipWith (-) a115390_list
(tail $ map (* 2) $ zipWith (-) a115390_list (tail a115390_list)))
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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