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A165190
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G.f.: 1/((1-x^4)*(1-x^5)).
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3
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1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 4, 3, 3, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 5, 5, 4, 4, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 6
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OFFSET
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0,21
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COMMENTS
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A121262 convolved with A079998. The two sequences have very simple generating functions and can be mapped to the numeric partitions 4=4 and 5=5 respectively.
Number of partitions of n into parts 4 and 5. - Joerg Arndt, Aug 28 2015
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LINKS
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FORMULA
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1 followed by the Euler transform of the finite sequence [0,0,0,1,1].
G.f.: 1/((1-x)^2*(1+x)*(1+x^2)*(1+x+x^2+x^3+x^4)). [R. J. Mathar, Oct 07 2009]
a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=1, a(5)=1, a(6)=0, a(7)=0, a(8)=1, a(n) = a(n-4)+a(n-5)-a(n-9), n>8. - Harvey P. Dale, Aug 16 2012
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MAPLE
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MATHEMATICA
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CoefficientList[Series[1/((1-x^4)(1-x^5)), {x, 0, 110}], x] (* or *) LinearRecurrence[{0, 0, 0, 1, 1, 0, 0, 0, -1}, {1, 0, 0, 0, 1, 1, 0, 0, 1}, 110] (* Harvey P. Dale, Aug 16 2012 *)
Table[Floor[(n + 4)/4] - Floor[(n + 4)/5], {n, 0, 100}] (* Wesley Ivan Hurt, Aug 27 2015 *)
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PROG
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(Magma) [Floor((n+4)/4) - Floor((n+4)/5) : n in [0..100]]; // Wesley Ivan Hurt, Aug 27 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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Removed duplicate of comment in A165188; Euler transform formula corrected - R. J. Mathar, Oct 07 2009
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STATUS
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approved
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