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1, 0, 3, 1, 6, 3, 11, 6, 18, 11, 27, 18, 39, 27, 54, 39, 72, 54, 94, 72, 120, 94, 150, 120, 185, 150, 225, 185, 270, 225, 321, 270, 378, 321, 441, 378, 511, 441, 588, 511, 672, 588, 764, 672, 864, 764, 972, 864, 1089, 972, 1215, 1089, 1350, 1215, 1495, 1350
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| This sequence convolved with A000217 (without initial term 0) yields A164680.
See A164680 for similar convolutions.
Contribution from Alford Arnold (Alford1940(AT)aol.com), Sep 24 2009: (Start)
A165188 convolved with A000217 yields sequence A164680. This is to be expected
since A000217 can be associated with partition 1+1+1, A164680 with partition
1+1+1+2+2+2+3 and A165188 with partition 2+2+2+3 by observing their unreduced
generating functions and verified by generating the sequences
by converting the partitions into finite sequences and using Euler's
Transform.
Thus partition 1+1+1 yields the finite sequence (3);
partition 2+2+2+3 yields the finite sequence (0,3,1);
and, when combined, partition 1+1+1+2+2+2+3 yields (3,3,1).
(End)
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FORMULA
| a(n) = -a(n-1)+2*a(n-2)+3*a(n-3)-3*a(n-5)-2*a(n-6)+a(n-7)+a(n-8)+1 for n > 8; a(1)=1, a(2)=0, a(3)=3, a(4)=1, a(5)=6, a(6)=3, a(7)=11, a(8)=6. [From Klaus Brockhaus, Sep 15 2009]
G.f.: (x/((1-x)^4*(1+x)^3*(1+x+x^2)). [From Klaus Brockhaus, Sep 15 2009]
a(n)= (2*n^3+21*n^2+63*n+49)/288-(-1)^n*(9+7*n+n^2)/32+A057078(n)/9. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 17 2009]
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EXAMPLE
| A014125 begins 1,3,6,11,18,27,..., thus this sequence begins 1,0,3,1,6,3,11,6,18,11,27,18,... .
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PROG
| (PARI) /* first computes u = A014125 as second bisection of A001400, then interleaves */ {m=28; u=vector(m, n, polcoeff(1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))+O(x^(2*n)), 2*n-1)); vector(2*m, k, if(k%2==1, u[(k+1)/2], if(k==2, 0, u[k/2-1])))} [From Klaus Brockhaus, Sep 15 2009]
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CROSSREFS
| Cf. A014125, A000217, A164680, A001400.
Sequence in context: A158822 A121443 A008795 * A132180 A126191 A070883
Adjacent sequences: A165185 A165186 A165187 * A165189 A165190 A165191
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KEYWORD
| nonn
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AUTHOR
| Alford Arnold (Alford1940(AT)aol.com), Sep 13 2009
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EXTENSIONS
| Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 15 2009
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