0,2

Number of (s(0), s(1), ..., s(n+2)) such that 0 < s(i) < 6 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n+2, s(0) = 1, s(n+2) = 3. - Herbert Kociemba (kociemba(AT)t-online.de), Jun 17 2004

A Whitney transform of 2^n (see Benoit Cloitre formula and A004070). The Whitney transform maps the sequence with g.f. g(x) to that with g.f. (1/(1-x))g(x(1+x)). - Paul Barry (pbarry(AT)wit.ie), Feb 16 2005

F. R. K. Chung and R. L. Graham, Primitive juggling sequences, preprint, 2006.

a(n) = 3*a(n-1)-2*a(n-3) = 2*A057960(n)-1 = round[2*A028859(n)/sqrt(3)-1/3] = sum_i(b(n, i)) where b(n, 0)=b(n, 6)=0, b(0, 3)=1, b(0, i)=0 if i<>3 and b(n+1, i)=b(n, i-1)+b(n, i)+b(n, i+1) if 0<i<6 [i.e. the number of three-choice paths along a corridor width 5, starting from the middle]. - Henry Bottomley (se16(AT)btinternet.com), Mar 06 2003

Binomial transform of A068911. a(n)=(1+sqrt(3))^n(2+sqrt(3))/3+(1-sqrt(3))^n(2-sqrt(3))/3-1/3 - Paul Barry (pbarry(AT)wit.ie), Feb 17 2004

a(0)=1, for n>=1 a(n)=ceil((1+sqrt(3))*a(n-1)). - Benoit Cloitre, Jun 19 2004.

a(n)=sum(i=0, n, sum(j=0, n, 2^j*binomial(j, i-j))) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 23 2004

(PARI) a(n)=sum(i=0, n, sum(j=0, n, 2^j*binomial(j, i-j)))

First differences are in A080953.

Adjacent sequences: A077843 A077844 A077845 this_sequence A077847 A077848 A077849

Sequence in context: A069403 A094292 A000242 this_sequence A005322 A103780 A098182

nonn,easy

njas, Nov 17 2002