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A165189
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Partial sums of partial sums of (A001840 interleaved with zeros).
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0
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1, 2, 5, 8, 14, 20, 31, 42, 60, 78, 105, 132, 171, 210, 264, 318, 390, 462, 556, 650, 770, 890, 1040, 1190, 1375, 1560, 1785, 2010, 2280, 2550, 2871, 3192, 3570, 3948, 4389, 4830, 5341, 5852, 6440, 7028, 7700, 8372, 9136, 9900, 10764, 11628, 12600, 13572
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also convolution of period six sequence 1,0,0,0,0,0,1,... (A079979) with sequence 1,2,5,8,14,20,30,40,... (A006918 without initial zero).
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FORMULA
| G.f.: x/((1-x)^5*(1+x)^3*(1-x+x^2)*(1+x+x^2)).
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EXAMPLE
| A001840 interleaved with zeros is
1, 0, 2, 0, 3, 0, 5, 0, 7, 0, 9, 0, 12, 0, 15, 0, ...
Partial sums thereof are
1, 1, 3, 3, 6, 6, 11, 11, 18, 18, 27, 27, 39, 39, 54, 54, ...
This equals A014125 interleaved with itself.
Partial sums thereof are
1, 2, 5, 8, 14, 20, 31, 42, 60, 78, 105, 132, 171, 210, 264, 318, ...
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PROG
| (PARI) /* first computes u = A001840 interleaved with zeros, then v = partial sums, then w = second partial sums */ {m=50; u=vector(m, n, polcoeff(x/((1-x^2)^3*(1+x^2+x^4))+x*O(x^(n)), n)); v=vector(m); a=u[1]; v[1]=a; for(n=2, m, a+=u[n]; v[n]=a); w=vector(m-1); a=v[1]; w[1]=a; for(n=2, m-1, a+=v[n]; w[n]=a); w} [From Klaus Brockhaus, Sep 21 2009]
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CROSSREFS
| Cf. A001840 (expansion of x/((1-x)^3*(1+x+x^2))), A001840 (expansion of x/((1-x)^2*(1-x^3))), A000004 (zero sequence), A079979, A006918, A014125.
Sequence in context: A095348 A022907 A006918 * A011842 A000094 A058578
Adjacent sequences: A165186 A165187 A165188 * A165190 A165191 A165192
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KEYWORD
| nonn
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AUTHOR
| Alford Arnold (Alford1940(AT)aol.com), Sep 16 2009
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EXTENSIONS
| Edited and corrected by R. J. Mathar, Klaus Brockhaus and N. J. A. Sloane, Sep 21 2009 - Sep 25 2009
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