cp's OEIS Frontend

A049112 2-ranks of difference sets constructed from Glynn type I hyperovals.

%I A049112 #15 Sep 08 2022 08:44:58
%S A049112 1,1,3,7,13,23,45,87,167,321,619,1193,2299,4431,8541,16463,31733,
%T A049112 61167,117903,227265,438067,844401,1627635,3137367,6047469,11656871,
%U A049112 22469341,43311047,83484727,160921985,310187099,597904857,1152498667
%N A049112 2-ranks of difference sets constructed from Glynn type I hyperovals.
%H A049112 G. C. Greubel, <a href="/A049112/b049112.txt">Table of n, a(n) for n = 1..1000</a>
%H A049112 R. Evans, H. Hollmann, C. Krattenthaler and Q. Xiang, <a href="http://dx.doi.org/10.1006/jcta.1998.2950">Gauss sums, Jacobi sums, and p-ranks of cyclic difference sets</a>, J. Combin. Theory Ser. A, 87.1 (1999), 74-119.
%H A049112 Ronald Evans, Henk Hollmann, Christian Krattenthaler, and Qing Xiang, <a href="https://www.mat.univie.ac.at/~kratt/artikel/glynn.html">Supplement to "Gauss Sums, Jacobi Sums and p-ranks ..."</a>
%H A049112 Q. Xiang, <a href="https://doi.org/10.1109/18.737547">On Balanced Binary Sequences with Two-Level Autocorrelation Functions</a>, IEEE Trans. Inform. Theory 44 (1998), 3153-3156.
%F A049112 G.f.: (1-x+x^2+x^3-x^4-2*x^5)/(1-2*x+x^5).
%F A049112 a(n+1) = a(n) + a(n-1) + a(n-2) + a(n-3) - 1, n >= 5.
%p A049112 L := 1,1,3,7,13: for i from 6 to 140 do l := nops([ L ]): L := L,op(l,[ L ])+op(l-1,[ L ])+op(l-2,[ L ])+op(l-3,[ L ])-1: od: [ L ];
%t A049112 Join[{1,1,3,7}, Table[a[1]=3; a[2]=1; a[3]=3; a[4]=7; a[i]=a[i-1]+a[i-2] +a[i-3]+a[i-4] -1, {i,5,40}]]
%t A049112 CoefficientList[Series[(1-x+x^2+x^3-x^4-2*x^5)/(1-2*x+x^5), {x,0,40}], x] (* _G. C. Greubel_, Jul 10 2019 *)
%o A049112 (PARI) my(x='x+O('x^40)); Vec((1-x+x^2+x^3-x^4-2*x^5)/(1-2*x+x^5)) \\ _G. C. Greubel_, Jul 10 2019
%o A049112 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x+x^2+x^3-x^4-2*x^5)/(1-2*x+x^5) )); // _G. C. Greubel_, Jul 10 2019
%o A049112 (Sage) ((1-x+x^2+x^3-x^4-2*x^5)/(1-2*x+x^5)).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Jul 10 2019
%o A049112 (GAP) a:=[1,3,7,13];; for n in [5..40] do a[n]:=a[n-1]+a[n-2]+a[n-3] +a[n-4] -1; od; Concatenation([1], a); # _G. C. Greubel_, Jul 10 2019
%Y A049112 Cf. A001595, A049114.
%K A049112 nonn,easy
%O A049112 1,3
%A A049112 Christian Krattenthaler (kratt(AT)ap.univie.ac.at)