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

0,2

Links

Table of n, a(n) for n=0..36.

Rémy Sigrist, PARI program for A274005

Example

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.

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

Prog

(PARI) See Links section.

Crossrefs

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

Cf. A362063.

Sequence in context: A248847 A059173 A355520 * A027560 A135493 A216241

Adjacent sequences: A274002 A274003 A274004 * A274006 A274007 A274008

Keyword

nonn

Author

Jeffrey Shallit, Jun 06 2016

Extensions

More terms from Rémy Sigrist, Jun 24 2021

Status

approved