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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

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: A180224 A173412 A079818 * A005056 A014143 A077994

Adjacent sequences:  A115387 A115388 A115389 * A115391 A115392 A115393

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Mar 08 2006

EXTENSIONS

More terms from Farideh Firoozbakht, Mar 11 2006

STATUS

approved

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Last modified December 6 10:58 EST 2016. Contains 278776 sequences.