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.

1, 2, 4, 8, 16, 32, 62, 120, 222, 410, 728, 1294, 2220, 3816, 6380, 10690, 17486, 28704, 46180, 74464, 118226, 188158, 295062, 464146, 721500, 1123384, 1731646, 2676538, 4094776, 6279380, 9562698, 14563312, 22043302, 33433502, 50357062, 75988618, 114092544

Offset: 0

Author

Jeffrey Shallit, Jun 06 2016

Keywords

• nonn

Examples

			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.
		

Links

• Rémy Sigrist, PARI program for A274005

Crossrefs

Cf. A005598, which is the analogous sequence where "2" is replaced by "1".

Cf. A362063.

Programs

Maple

A274005 := proc(n)
    local a,b,lbdgs,bdgs,i,j,wrks,stri ;
    a := 0 ;
    for b from 0 to 2^n-1  do
        bdgs := convert(b,base,2) ;
        lbdgs := nops(bdgs) ;
        bdgs := [op(bdgs),seq(0,i=1..n-lbdgs)] ;
        wrks := true;
        for stri from 3 to n/2 do
            for i from 1 to n-stri do
            for j from i+1 to n-stri+1 do
                if abs(add(bdgs[u],u=i..i+stri-1) - add(bdgs[u],u=j..j+stri-1)) >2 then
                    wrks := false;
                end if ;
                if not wrks then
                    break;
                end if;
            end do:
            end do:
            if not wrks then
                break;
            end if;
        end do ;
        if wrks then
            a := a+1 ;
        end if;
    end do:
    a ;
end proc: # R. J. Mathar, Jun 16 2016

PARI

See Links section.

Extensions

More terms from Rémy Sigrist, Jun 24 2021