A011746 Expansion of (1 + x^2)/(1 + x^2 + x^5) mod 2.
1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1
Offset: 0
Links
- Michael Gilleland, Some Self-Similar Integer Sequences
- R. Gold, Characteristic linear sequences and their coset functions, J. SIAM Applied. Math., 14 (1966), 980-985.
- Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
Crossrefs
Programs
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Maple
series((1+x^2)/(1+x^2+x^5),x,100) mod 2;
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Mathematica
Mod[CoefficientList[Series[(1+x^2)/(1+x^2+x^5),{x,0,80}],x],2] (* Harvey P. Dale, Jul 19 2023 *) -
PARI
A011746_vec=Vec((1+x^2)/(1+x^2+x^5)+O(x^31))%2 \\ For illustrative purpose. A011746(n)=bittest(377253537,n%31) \\ M. F. Hasler, Feb 17 2018
Formula
a(n) = A088002(n) mod 2. - R. J. Mathar, May 26 2008
G.f.: (1+x^5+x^7+x^9+x^10+x^11+x^13+x^14+x^18+x^19+x^20+x^21+x^22+x^25+x^26+x^28)/(1-x^31). - Robert Israel, May 06 2018
a(n) = A011662(n-1). - R. J. Mathar, Jan 12 2024