cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A147592 Expansion of 1/(1 + x - x^2 - 3*x^3 - x^4 + x^5 + x^6).

This page as a plain text file.
%I A147592 #16 Oct 26 2022 03:05:02
%S A147592 1,-1,2,0,0,4,-2,5,3,0,12,0,12,16,5,35,18,36,64,40,110,105,135,240,
%T A147592 216,384,472,560,905,999,1458,1960,2368,3500,4302,5805,7947,9936,
%U A147592 13860,17920,23588,32096,41229,55755,73570,96460,129920,169680,226206,300369
%N A147592 Expansion of 1/(1 + x - x^2 - 3*x^3 - x^4 + x^5 + x^6).
%H A147592 G. C. Greubel, <a href="/A147592/b147592.txt">Table of n, a(n) for n = 0..1000</a>
%H A147592 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-1,1,3,1,-1,-1).
%F A147592 G.f.: -1/(x^3*f(x)*f(1/x)), where f(x) = -1 - x + x^3.
%F A147592 G.f.: 1/((1+x-x^3)*(1-x^2-x^3)). - _Colin Barker_, Nov 04 2012
%t A147592 f[x_]= x^3-x-1; CoefficientList[Series[-1/(x^3*f[x]*f[1/x]), {x,0,60}], x]
%t A147592 LinearRecurrence[{-1,1,3,1,-1,-1},{1,-1,2,0,0,4},60] (* _Harvey P. Dale_, Sep 23 2020 *)
%o A147592 (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( 1/((1+x-x^3)*(1-x^2-x^3)) )); // _G. C. Greubel_, Oct 25 2022
%o A147592 (SageMath)
%o A147592 def A147592_list(prec):
%o A147592     P.<x> = PowerSeriesRing(ZZ, prec)
%o A147592     return P( 1/((1+x-x^3)*(1-x^2-x^3)) ).list()
%o A147592 A147592_list(60) # _G. C. Greubel_, Oct 25 2022
%Y A147592 Cf. A147593, A147598, A147605, A147606.
%K A147592 sign,easy
%O A147592 0,3
%A A147592 _Roger L. Bagula_, Nov 08 2008
%E A147592 Edited by _Joerg Arndt_ and _Colin Barker_, Nov 04 2012