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A049114 2-ranks of difference sets constructed from Glynn type II hyperovals. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

R. Evans, H. D. L. Hollmann, C. Krattenthaler, Q. Xiang, Gauss Sums, Jacobi Sums and p-Ranks of Cyclic Difference Sets, J. Combin. Theory Ser. A 87 (1999), 74-119.

Q. Xiang, On Balanced Binary Sequences with Two-Level Autocorrelation Functions, IEEE Trans. Inform. Theory 44 (1998), 3153-3156.

LINKS

Table of n, a(n) for n=1..31.

Supplement to "Gauss Sums, Jacobi Sums and p-ranks ..."

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, 100} ] ]

CROSSREFS

Cf. A001595, A049112.

Sequence in context: A002596 A098597 A097038 * A179189 A030735 A162462

Adjacent sequences:  A049111 A049112 A049113 * A049115 A049116 A049117

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified February 24 17:22 EST 2018. Contains 299624 sequences. (Running on oeis4.)