Search: id:A049114
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%I A049114
%S A049114 1,1,5,7,21,37,89,173,383,777,1665,3441,7277,15159,31885,66645,139865,
%T A049114 292757,613823,1285585,2694433,5644609,11828501,24782311,51928773,
%U A049114 108802597,227978105,477674813,1000877759,2097121497,4394101857
%N A049114 2-ranks of difference sets constructed from Glynn type II hyperovals.
%D A049114 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.
%D A049114 Q. Xiang, On Balanced Binary Sequences with Two-Level Autocorrelation 
               Functions, IEEE Trans. Inform. Theory 44 (1998), 3153-3156.
%H A049114 <a href="http://radon.mat.univie.ac.at/People/kratt/artikel/glynn.html">
               Supplement to "Gauss Sums, Jacobi Sums and p-ranks ..."</a>
%F A049114 G.f.: (1-x+x^2-x^3+x^4)/(1-2*x-2*x^2+4*x^3-x^5).
%F A049114 a(n+1) = a(n) + 3*a(n-1) - a(n-2) - a(n-3) + 1.
%p A049114 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 ];
%t A049114 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} ] ]
%Y A049114 Cf. A001595, A049112.
%Y A049114 Sequence in context: A002596 A098597 A097038 this_sequence A030735 A162462 
               A165144
%Y A049114 Adjacent sequences: A049111 A049112 A049113 this_sequence A049115 A049116 
               A049117
%K A049114 nonn,easy
%O A049114 1,3
%A A049114 Christian Krattenthaler (kratt(AT)ap.univie.ac.at)

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