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

1,3

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.

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.

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 ];

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 *)

Prog

(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
(Magma) R<x>:=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
(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
(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

Crossrefs

Cf. A001595, A049112.

Sequence in context: A002596 A098597 A097038 * A179189 A030735 A303189

Adjacent sequences: A049111 A049112 A049113 * A049115 A049116 A049117

Keyword

nonn,easy

Author

Christian Krattenthaler (kratt(AT)ap.univie.ac.at)

Status

approved