login
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, 895042726912, 2541282959872
OFFSET
0,4
COMMENTS
See also A117189 Binomial transform of the tribonacci sequence A000073.
LINKS
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
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 08 2006
STATUS
approved