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A099463 Bisection of tribonacci numbers. 8
0, 1, 2, 7, 24, 81, 274, 927, 3136, 10609, 35890, 121415, 410744, 1389537, 4700770, 15902591, 53798080, 181997601, 615693474, 2082876103, 7046319384, 23837527729, 80641778674, 272809183135, 922906855808, 3122171529233 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Binomial transform of A099462.

a(n+1) gives row sums of number triangle A114123 or A184883. Partial sums are A113300. - Paul Barry, Feb 07 2006

LINKS

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (3,1,1)

FORMULA

G.f.: x(1-x)/(1-3x-x^2-x^3); a(n)=sum{k=0..n, binomial(n, k)*sum{j=0..floor((k-1)/2), binomial(j, k-2j-1)4^j}}.

a(n)=3a(n-1)+a(n-2)+a(n-3); a(n)=sum{k=0..n, sum{j=0..n, C(2k,n-k-j)*C(n-k,j)*2^(n-k-j)}}. - Paul Barry, Feb 07 2006

a(n)/a(n-1) tends to 3.38297576....the square of the tribonacci constant A058265 . - Gary W. Adamson, Feb 28 2006

If p[1]=2, p[2]=3, p[i]=4, (i>2), and if A is Hessenberg matrix of order n defined by: A[i,j]=p[j-i+1], (i<=j), A[i,j]=-1, (i=j+1), and A[i,j]=0 otherwise. Then, for n>=1, a(n+1)=det A. [From Milan Janjic, May 02 2010]

MATHEMATICA

LinearRecurrence[{3, 1, 1}, {0, 1, 2}, 30] (* or *) Join[{0}, Mean/@ Partition[ LinearRecurrence[ {1, 1, 1}, {1, 1, 1}, 60], 2]] (* Harvey P. Dale, Apr 02 2012 *)

CROSSREFS

Cf. A000073.

Sequence in context: A038765 A027126 A027128 * A021000 A003480 A020727

Adjacent sequences:  A099460 A099461 A099462 * A099464 A099465 A099466

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 16 2004

STATUS

approved

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Last modified January 17 10:30 EST 2019. Contains 319218 sequences. (Running on oeis4.)