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A049112
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2-ranks of difference sets constructed from Glynn type I hyperovals.
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3
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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
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OFFSET
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1,3
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LINKS
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FORMULA
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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.
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MAPLE
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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
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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 *)
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PROG
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(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
(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
(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
(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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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Christian Krattenthaler (kratt(AT)ap.univie.ac.at)
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STATUS
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approved
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