A069950 - OEIS

%I #15 Oct 01 2023 13:21:52

%S 1,1,3,4,7,11,17,25,38,53,77,105,146,196,265,350,462,600,778,994,1270,

%T 1601,2016,2514,3126,3857,4745,5797,7063,8554,10331,12411,14871,17734,

%U 21093,24986,29519,34747,40801,47746,55746,64884,75353

%N Expansion of (1+x^2)*(1+x^5)*(1+x^8)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)*(1-x^8)*(1-x^9)*(1-x^10)).

%H G. C. Greubel, <a href="/A069950/b069950.txt">Table of n, a(n) for n = 0..1000</a>

%H G. E. Andrews, P. Paule and A. Riese, <a href="https://doi.org/10.1006/aama.2001.0733">MacMahon's Partition Analysis VIII: Plane partition diamonds</a>, Advances Applied Math., 27 (2001), 231-242.

%H <a href="/index/Rec#order_48">Index entries for linear recurrences with constant coefficients</a>, signature (1, 2, -1, -2, 1, 1, -3, -1, 3, 1, -3, 2, 4, -1, -2, 1, -1, -3, -1, 0, 0, 0, 2, 2, 2, 0, 0, 0, -1, -3, -1, 1, -2, -1, 4, 2, -3, 1, 3, -1, -3, 1, 1, -2, -1, 2, 1, -1).

%F G.f.: (1+x^2)*(1+x^5)*(1+x^8)/( Product_{j=1..10} (1-x^j) ). - _G. C. Greubel_, Aug 16 2022

%t CoefficientList[Series[(1+x^2)*(1+x^5)*(1+x^8)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4)/ (1-x^5)/(1-x^6)/(1-x^7)/(1-x^8)/(1-x^9)/(1-x^10),{x,0,60}],x] (* _Harvey P. Dale_, Feb 25 2013 *)

%o (PARI) Vec((1+x^2)*(1+x^5)*(1+x^8)/(1-x)/(1-x^2)/(1-x^3)/(1-x^4)/(1-x^5)/(1-x^6)/(1-x^7)/(1-x^8)/(1-x^9)/(1-x^10)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^2)*(1+x^5)*(1+x^8)/( (&*[1-x^j: j in [1..10]]) ) )); // _G. C. Greubel_, Aug 16 2022

%o (Sage)

%o def A069950_list(prec):

%o     P.<x> = PowerSeriesRing(ZZ, prec)

%o     return P( (1+x^2)*(1+x^5)*(1+x^8)/product(1-x^j for j in (1..10)) ).list()

%o A069950_list(60) # _G. C. Greubel_, Aug 16 2022

%Y Cf. A008763, A060962.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, May 05 2002