1,2

Number of representations of n as a sum of Jacobsthal numbers (1 is allowed twice as a part). Partial sums are A003159. With interpolated zeros, g.f. is Product{k>=1, 1+x^A078008(k)}/2. - Paul Barry (pbarry(AT)wit.ie), Dec 09 2004

Can also be generated by counting the consecutive 0's or 1's in A010060 or A010059. - Robin D. Saunders (saunders_robin_d(AT)hotmail.com), Sep 06 2006

J.-P. Allouche, Andre Arnold, Jean Berstel, Srecko Brlek, William Jockusch, Simon Plouffe and Bruce E. Sagan, A sequence related to that of Thue-Morse, Discrete Math., 139 (1995), 455-461.

S. Brlek, Enumeration of factors in the Thue-Morse word, Discrete Applied Math., 24 (1989), 83-96.

It appears that the sequence can be calculated by any of the following three methods: (1) Start with 1 and repeatedly replace 1 with 1, 2, 1 and 2 with 1, 2, 2, 2, 1; (2) a(1)=1, all terms are either 1 or 2 and, for n>0, a(n)=1 if the length of the n-th run of 2's is 1; a(n)=2 if the length of the n-th run of consecutive 2's is 3, with each run of 2's separated by a run of two 1's; (3) replace each 3 in A080426 with 2. - John W. Layman (layman(AT)math.vt.edu), Feb 18 2003

a(1)=1, for n>1 a(n)= A003159(n)-A003159(n-1) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 31 2003

G.f.: Product{k>=1, 1+x^A001045(k)} - Paul Barry (pbarry(AT)wit.ie), Dec 09 2004

Cf. A101615.

Sequence in context: A023191 A029256 A109073 this_sequence A051486 A081355 A060778

Adjacent sequences: A026462 A026463 A026464 this_sequence A026466 A026467 A026468

nonn

Clark Kimberling (ck6(AT)evansville.edu)

Corrected and extended by John W. Layman (layman(AT)math.vt.edu), Feb 18 2003