login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 * A358055 A011842 A000094
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)