A049112 2-ranks of difference sets constructed from Glynn type I hyperovals.
1, 1, 3, 7, 13, 23, 45, 87, 167, 321, 619, 1193, 2299, 4431, 8541, 16463, 31733, 61167, 117903, 227265, 438067, 844401, 1627635, 3137367, 6047469, 11656871, 22469341, 43311047, 83484727, 160921985, 310187099, 597904857, 1152498667
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:=[1,3,7,13];; 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
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Magma
R
:=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 -
Maple
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 ];
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Mathematica
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}]] 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 *) -
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 -
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
Formula
G.f.: (1-x+x^2+x^3-x^4-2*x^5)/(1-2*x+x^5).
a(n+1) = a(n) + a(n-1) + a(n-2) + a(n-3) - 1, n >= 5.