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 A165189 Partial sums of partial sums of (A001840 interleaved with zeros). 0
 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; text; internal format)
 OFFSET 1,2 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). LINKS Index entries for linear recurrences with constant coefficients, signature (2, 1, -4, 1, 2, 0, -2, -1, 4, -1, -2, 1). FORMULA G.f.: x/((1-x)^5*(1+x)^3*(1-x+x^2)*(1+x+x^2)). 54*a(n) = 631/64 +405/16*n +3/32*n^4 +15/8*n^3 +381/32*n^2 -(-1)^n*( 9/32*n^2 +45/16*n +375/64) -A131713(n) -3*A057079(n). - R. J. Mathar, Jun 16 2018 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, ... MATHEMATICA Drop[Accumulate[Accumulate[Riffle[LinearRecurrence[{2, -1, 1, -2, 1}, {0, 1, 2, 3, 5}, 30], 0]]], 2] (* or *) LinearRecurrence[{2, 1, -4, 1, 2, 0, -2, -1, 4, -1, -2, 1}, {1, 2, 5, 8, 14, 20, 31, 42, 60, 78, 105, 132}, 50] (* Harvey P. Dale, Jun 08 2018 *) 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} \\ Klaus Brockhaus, Sep 21 2009 CROSSREFS Cf. A001840 (expansion of x/((1-x)^3*(1+x+x^2))), A001840 (expansion of x/((1-x)^2*(1-x^3))), A079979, A006918, A014125. Sequence in context: A022907 A006918 A274523 * A011842 A000094 A182377 Adjacent sequences:  A165186 A165187 A165188 * A165190 A165191 A165192 KEYWORD nonn AUTHOR Alford Arnold, Sep 16 2009 EXTENSIONS Edited and corrected by R. J. Mathar, Klaus Brockhaus and N. J. A. Sloane, Sep 21 2009 - Sep 25 2009 STATUS approved

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Last modified February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)