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 A115390 Binomial transform of tribonacci sequence A000073. 6
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS See also A117189 Binomial transform of the tribonacci sequence A000073. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..1000 J. Pan, Multiple Binomial Transforms and Families of Integer Sequences , J. Int. Seq. 13 (2010), 10.4.2 J. Pan, Some Properties of the Multiple Binomial Transform and the Hankel Transform of Shifted Sequences , J. Int. Seq. 14 (2011) # 11.3.4, remark 14. Eric Weisstein's World of Mathematics, Binomial Transform. Index entries for linear recurrences with constant coefficients, signature (4, -4, 2). FORMULA 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 EXAMPLE 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. MATHEMATICA 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 *) PROG (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))) -- Reinhard Zumkeller, Oct 21 2011 CROSSREFS Cf. A000073, A117189. Trisection of A103685. Sequence in context: A293005 A173412 A079818 * A005056 A014143 A077994 Adjacent sequences:  A115387 A115388 A115389 * A115391 A115392 A115393 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Mar 08 2006 STATUS approved

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Last modified January 23 04:16 EST 2020. Contains 331168 sequences. (Running on oeis4.)