A115390 Binomial transform of tribonacci sequence A000073.

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

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 A361476

Adjacent sequences: A115387 A115388 A115389 * A115391 A115392 A115393

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 08 2006

Status

approved