cp's OEIS Frontend

A274005 Number of length-n binary sequences where the sum of each subblock differs by at most 2 from every other subblock of the same length.

%I A274005 #18 May 19 2023 08:02:12
%S A274005 1,2,4,8,16,32,62,120,222,410,728,1294,2220,3816,6380,10690,17486,
%T A274005 28704,46180,74464,118226,188158,295062,464146,721500,1123384,1731646,
%U A274005 2676538,4094776,6279380,9562698,14563312,22043302,33433502,50357062,75988618,114092544
%N A274005 Number of length-n binary sequences where the sum of each subblock differs by at most 2 from every other subblock of the same length.
%H A274005 Rémy Sigrist, <a href="/A274005/a274005.gp.txt">PARI program for A274005</a>
%e A274005 For n = 6, the strings 000111 and 111000 are not counted, since the sum of length-3 subblocks that begin and end differ by 3.
%p A274005 A274005 := proc(n)
%p A274005     local a,b,lbdgs,bdgs,i,j,wrks,stri ;
%p A274005     a := 0 ;
%p A274005     for b from 0 to 2^n-1  do
%p A274005         bdgs := convert(b,base,2) ;
%p A274005         lbdgs := nops(bdgs) ;
%p A274005         bdgs := [op(bdgs),seq(0,i=1..n-lbdgs)] ;
%p A274005         wrks := true;
%p A274005         for stri from 3 to n/2 do
%p A274005             for i from 1 to n-stri do
%p A274005             for j from i+1 to n-stri+1 do
%p A274005                 if abs(add(bdgs[u],u=i..i+stri-1) - add(bdgs[u],u=j..j+stri-1)) >2 then
%p A274005                     wrks := false;
%p A274005                 end if ;
%p A274005                 if not wrks then
%p A274005                     break;
%p A274005                 end if;
%p A274005             end do:
%p A274005             end do:
%p A274005             if not wrks then
%p A274005                 break;
%p A274005             end if;
%p A274005         end do ;
%p A274005         if wrks then
%p A274005             a := a+1 ;
%p A274005         end if;
%p A274005     end do:
%p A274005     a ;
%p A274005 end proc: # _R. J. Mathar_, Jun 16 2016
%o A274005 (PARI) See Links section.
%Y A274005 Cf. A005598, which is the analogous sequence where "2" is replaced by "1".
%Y A274005 Cf. A362063.
%K A274005 nonn
%O A274005 0,2
%A A274005 _Jeffrey Shallit_, Jun 06 2016
%E A274005 More terms from _Rémy Sigrist_, Jun 24 2021