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A096386
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Expansion of x^2(x^4+x^2+x+1)/(x^7-x^6-x+1).
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0
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0, 0, 1, 2, 3, 3, 4, 4, 5, 6, 7, 7, 8, 8, 9, 10, 11, 11, 12, 12, 13, 14, 15, 15, 16, 16, 17, 18, 19, 19, 20, 20, 21, 22, 23, 23, 24, 24, 25, 26, 27, 27, 28, 28, 29, 30, 31, 31, 32, 32, 33, 34, 35, 35, 36, 36, 37, 38, 39, 39, 40, 40, 41, 42, 43, 43, 44, 44, 45, 46, 47, 47, 48, 48
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| First differences are 6-periodic.
Number of numbers <= n which are divisible by 2 or 3. - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 13 2007
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REFERENCES
| S. Ramanujan, Question 723, Collected Papers of Srinivasa Ramanujan, p. 332, Ed. G. H. Hardy et al., AMS Chelsea 2000.
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LINKS
| Index entries for two-way infinite sequences
S. Ramanujan, Question 723, J. Ind. Math. Soc.
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FORMULA
| a(n) = [n/2] + [(n+3)/6] = [n/3] + [(n+2)/6] + [(n+4)/6].
G.f.: x^2(1+x+x^2+x^4)/((1-x)(1-x^6)). a(-n)=-a(n-1)-1. a(n)=4+a(n-6).
a(n)=sum{k=0..n}{(1/90)*(-11*(k mod 6)+19*((k+1) mod 6)+4*((k+2) mod 6)+4*((k+3) mod 6)-11*((k+4) mod 6)+19*((k+5) mod 6)))-1} - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 25 2007
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PROG
| (PARI) a(n) = floor(n/2) + floor((n+3)/6)
(PARI) a(n)=n\2+(n+3)\6
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CROSSREFS
| Sequence in context: A005206 A057365 A014245 * A135671 A079420 A076895
Adjacent sequences: A096383 A096384 A096385 * A096387 A096388 A096389
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KEYWORD
| nonn,easy
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AUTHOR
| Ralf Stephan, Aug 05 2004
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