This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A008815 Expansion of (1+x^8)/((1-x)^2*(1-x^8)). 9
 1, 2, 3, 4, 5, 6, 7, 8, 11, 14, 17, 20, 23, 26, 29, 32, 37, 42, 47, 52, 57, 62, 67, 72, 79, 86, 93, 100, 107, 114, 121, 128, 137, 146, 155, 164, 173, 182, 191, 200, 211, 222, 233, 244, 255, 266, 277, 288, 301, 314, 327, 340, 353, 366, 379, 392, 407, 422 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,1,-2,1). FORMULA G.f.: (1 + x^8)/((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x^4)). a(n) = floor( (n*(n+2) + 14 + 4*((n mod 4) - 1)*(-1)^floor(n/4))/8 ). - Tani Akinari, Jul 25 2013 a(n) = 2*a(n-1) - a(n-2) + a(n-8) - 2*a(n-9) + a(n-10). - Vincenzo Librandi, May 14 2019 MAPLE seq(coeff(series((1+x^8)/((1-x)^2*(1-x^8)), x, n+1), x, n), n = 0..50); # G. C. Greubel, Sep 12 2019 MATHEMATICA CoefficientList[Series[(1+x^8)/(1-x)^2/(1-x^8), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 1, -2, 1}, {1, 2, 3, 4, 5, 6, 7, 8, 11, 14}, 50] (* Harvey P. Dale, Dec 17 2016 *) PROG (PARI) a(n)=(n*(n+2)+14+4*(n%4-1)*(-1)^(n\4))\8  \\ Tani Akinari, Jul 25 2013 (MAGMA) I:=[1, 2, 3, 4, 5, 6, 7, 8, 11, 14]; [n le 10 select I[n] else 2*Self(n-1) -Self(n-2)+Self(n-8)-2*Self(n-9)+Self(n-10): n in [1..50]]; // Vincenzo Librandi, May 14 2019 (Sage) def A008815_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P((1+x^8)/((1-x)^2*(1-x^8))).list() A008815_list(50) # G. C. Greubel, Sep 12 2019 (GAP) a:=[1, 2, 3, 4, 5, 6, 7, 8, 11, 14];; for n in [11..50] do a[n]:=2*a[n-1] -a[n-2]+a[n-8]-2*a[n-9]+a[n-10]; od; a; # G. C. Greubel, Sep 12 2019 CROSSREFS Cf. Expansions of the form (1+x^m)/((1-x)^2*(1-x^m)): A000290 (m=1), A000982 (m=2), A008810 (m=3), A008811 (m=4), A008812 (m=5), A008813 (m=6), A008814 (m=7), this sequence (m=8), A008816 (m=9), A008817 (m=10). Sequence in context: A067133 A192588 A258946 * A298434 A200371 A246025 Adjacent sequences:  A008812 A008813 A008814 * A008816 A008817 A008818 KEYWORD nonn,easy AUTHOR STATUS approved

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

Last modified December 12 09:36 EST 2019. Contains 329953 sequences. (Running on oeis4.)