0,2

Binomial transform of A001519. Case k=2 of family of recurrences a(n)=(2k+1)a(n-1)-A028387(k-1)a(n-2), a(0)=1,a(1)=k+1.

Number of (s(0), s(1), ..., s(2n+1)) such that 0 < s(i) < 10 and |s(i) - s(i-1)| = 1 for i = 1,2,....,2n+1, s(0) = 3, s(2n+1) = 4.

a(n+1) gives the number of periodic multiplex juggling sequences of length n with base state <2>. - Steve Butler (sbutler(AT)math.ucsd.edu), Jan 21 2008

a(n) is also the number of idempotent order-preserving partial transformations (of an n-element chain) of waist n (waist(alpha) = max(Im(alpha))). [From A. Umar (aumarh(AT)squ.edu.om), Sep 14 2008]

S. Butler and R. Graham, Enumerating (multiplex) juggling sequences, arXiv:0801.2597

Laradji, A. and Umar, A. Combinatorial results for semigroups of order-preserving partial transformations. Journal of Algebra 278, (2004), 342-359. [From A. Umar (aumarh(AT)squ.edu.om), Sep 14 2008]

a(n)=5a(n-1)-5a(n-2), a(0)=1, a(1)=3. a(n)=(1/2 - sqrt(5)/10)(5/2 - sqrt(5)/2)^n + (sqrt(5)/10 + 1/2)(sqrt(5)/2 + 5/2)^n. G.f.: (1-2x)/(1-5x+5x^2).

a(n-1)=sum(k=1, n, C(n, k)*F(k)^2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 26 2003

a(n)=A090041(n)/2^n - Paul Barry (pbarry(AT)wit.ie), Mar 23 2004

The sequence 0, 1, 3, 10, ... with a(n)=(5/2-sqrt(5)/2)^n/5+(5/2+sqrt(5)/2)^n/5-2(0)^n/5 is the binomial transform of F(n)^2 (A007598) - Paul Barry (pbarry(AT)wit.ie), Apr 27 2004

a(n)=sum{k=0..n, sum{j=0..n, C(n, j)C(j+k, 2k)}}; a(n)=sum{k=0..n, sum{j=0..n, C(n, k+j)*C(k, k-j)2^(n-k-j)}}; a(n)=sum{k=0..n, sum{j=0..n-k, C(n+k-j, n-k-j)C(k, j)(-1)^j*2^(n-k-j)}}; - Paul Barry (pbarry(AT)wit.ie), Nov 15 2005

Cf. A000045.

a(n) = 5*A052936(n-1), n>1.

Row sums of A114164.

a(n) = A111776(n, n) [From A. Umar (aumarh(AT)squ.edu.om), Sep 14 2008]

Sequence in context: A159309 A112107 A094855 this_sequence A026026 A047037 A134391

Adjacent sequences: A081564 A081565 A081566 this_sequence A081568 A081569 A081570

easy,nonn

Paul Barry (pbarry(AT)wit.ie), Mar 22 2003