A049114 2-ranks of difference sets constructed from Glynn type II hyperovals.
1, 1, 5, 7, 21, 37, 89, 173, 383, 777, 1665, 3441, 7277, 15159, 31885, 66645, 139865, 292757, 613823, 1285585, 2694433, 5644609, 11828501, 24782311, 51928773, 108802597, 227978105, 477674813, 1000877759, 2097121497, 4394101857
Offset: 1
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
- R. Evans, H. Hollmann, C. Krattenthaler and Q. Xiang, Gauss sums, Jacobi sums, and p-ranks of cyclic difference sets, J. Combin. Theory Ser. A, 87.1 (1999), 74-119.
- Ronald Evans, Henk Hollmann, Christian Krattenthaler, and Qing Xiang, Supplement to "Gauss Sums, Jacobi Sums and p-ranks ..."
- Q. Xiang, On Balanced Binary Sequences with Two-Level Autocorrelation Functions, IEEE Trans. Inform. Theory 44 (1998), 3153-3156.
Programs
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GAP
a:=[1,5,7,21];; for n in [5..40] do a[n]:=a[n-1]+3*a[n-2]-a[n-3] -a[n-4] +1; od; Concatenation([1], a); # G. C. Greubel, Jul 10 2019
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Magma
R
:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x+x^2-x^3+x^4)/(1-2*x-2*x^2+4*x^3-x^5) )); // G. C. Greubel, Jul 10 2019 -
Maple
L := 1,1,5,7: for i from 5 to 100 do l := nops([ L ]): L := L,op(l,[ L ])+3*op(l-1,[ L ])-op(l-2,[ L ])-op(l-3,[ L ])+1: od: [ L ];
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Mathematica
Join[{1,1,5,7}, Table[a[1]=1; a[2]=1; a[3]=5; a[4]=7; a[i]=a[i-1]+ 3*a[i-2]-a[i-3]-a[i-4] +1, {i, 5, 40}]] CoefficientList[Series[(1-x+x^2-x^3+x^4)/(1-2*x-2*x^2+4*x^3-x^5), {x, 0, 40}], x] (* G. C. Greubel, Jul 10 2019 *) -
PARI
my(x='x+O('x^40)); Vec((1-x+x^2-x^3+x^4)/(1-2*x-2*x^2+4*x^3-x^5)) \\ G. C. Greubel, Jul 10 2019 -
Sage
((1-x+x^2-x^3+x^4)/(1-2*x-2*x^2+4*x^3-x^5)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jul 10 2019
Formula
G.f.: (1-x+x^2-x^3+x^4)/(1-2*x-2*x^2+4*x^3-x^5).
a(n+1) = a(n) + 3*a(n-1) - a(n-2) - a(n-3) + 1.