A164457 - OEIS

%I #19 May 28 2026 00:05:58

%S 1,2,4,8,13,21,33,52,82,128,200,313,488,761,1188,1852,2887,4503,7020,

%T 10943,17063,26601,41468,64652,100792,157128,244965,381898,595363,

%U 928166,1446998,2255827,3516797,5482628,8547285,13325053,20773513,32385456,50488278

%N Number of binary strings of length n with no substrings equal to 0001, 0011, or 1010.

%H Alois P. Heinz, <a href="/A164457/b164457.txt">Table of n, a(n) for n = 0..2000</a> (first 500 terms from R. H. Hardin)

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2,-3,1).

%F G.f.: -(x^7-2*x^6+x^2+1)/((x-1)*(x^4-2*x^3-x+1)). - _R. J. Mathar_, Jan 19 2011

%t LinearRecurrence[{2,-1,2,-3,1},{1,2,4,8,13,21,33,52},40] (* _Harvey P. Dale_, Aug 19 2022 *)

%o (PARI) a(n)=if(n>2,([0,1,0,0,0; 0,0,1,0,0; 0,0,0,1,0; 0,0,0,0,1; 1,-3,2,-1,2]^(n-3)*[8;13;21;33;52])[1,1],[1,2,4][n+1]) \\ _Charles R Greathouse IV_, May 28 2026

%K nonn,easy

%O 0,2

%A _R. H. Hardin_, Aug 14 2009

%E Edited by _Alois P. Heinz_, Oct 12 2017