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.

A143335 Expansion of (1 - 2*x^3 - x^4 - 2*x^5 - x^6 - x^7 - x^8 + 2*x^9)/(1 + x - x^3 - x^4 - x^5 - x^6 - x^7 + x^9 + x^10).

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%I A143335 #24 Sep 08 2022 08:45:37
%S A143335 1,-1,1,-2,1,-2,0,-1,-3,2,-6,1,-4,-3,-3,-5,-4,-7,-6,-9,-8,-14,-10,-18,
%T A143335 -18,-20,-28,-27,-38,-39,-50,-57,-67,-79,-94,-109,-128,-154,-175,-213,
%U A143335 -244,-292,-341,-400,-475,-553,-655,-768,-905,-1062,-1253,-1470,-1732
%N A143335 Expansion of (1 - 2*x^3 - x^4 - 2*x^5 - x^6 - x^7 - x^8 + 2*x^9)/(1 + x - x^3 - x^4 - x^5 - x^6 - x^7 + x^9 + x^10).
%C A143335 Shares the same 10th-order "Salem" linear recurrence with A029826, A173243 and A125950.
%H A143335 G. C. Greubel, <a href="/A143335/b143335.txt">Table of n, a(n) for n = 0..1000</a>
%H A143335 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,1,1,1,1,1,0,-1,-1).
%F A143335 a(n) = -a(n-1) + a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7) - a(n-9) - a(n-10). - _Franck Maminirina Ramaharo_, Nov 02 2018
%p A143335 seq(coeff(series((1-2*x^3-x^4 -2*x^5-x^6-x^7-x^8+2*x^9)/(1+x-x^3-x^4-x^5-x^6-x^7 +x^9+x^10), x, n+1), x, n), n = 0..65); # _G. C. Greubel_, Mar 13 2020
%t A143335 LinearRecurrence[{-1,0,1,1,1,1,1,0,-1,-1}, {1,-1,1,-2,1,-2,0,-1,-3,2}, 65] (* _Franck Maminirina Ramaharo_, Nov 02 2018 *)
%o A143335 (PARI) my(x='x+O('x^65)); Vec((1-2*x^3-x^4-2*x^5-x^6-x^7-x^8+2*x^9)/(1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10)) \\ _G. C. Greubel_, Nov 03 2018
%o A143335 (Magma) R<x>:=PowerSeriesRing(Integers(), 65); Coefficients(R!( (1-2*x^3-x^4 -2*x^5-x^6-x^7-x^8+2*x^9)/(1+x-x^3-x^4-x^5-x^6-x^7+x^9 +x^10) )); // _G. C. Greubel_, Nov 03 2018
%Y A143335 Cf. A029826, A070178, A087612, A107479, A107480, A109538.
%Y A143335 Cf. A109543, A109544, A114749, A125950, A130844, A147851.
%K A143335 sign,easy
%O A143335 0,4
%A A143335 _Roger L. Bagula_ and _Gary W. Adamson_, Oct 22 2008
%E A143335 Edited by Assoc. Eds. of the OEIS - Jun 30 2010