A227186 Array A(n,k) read by antidiagonals: the length of the (k+1)-th run (k>=0) of binary digits of n, first run starting from the least significant bit of n.

0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0

Offset

0,10

Comments

A(n,k) is set to zero if there are less than k+1 runs.

The irregular table A101211 gives the nonzero terms of each row in reverse order. The terms on row n sum to A029837(n+1). The product of nonzero terms on row n>0 is A167489(n). Number of nonzero terms on each row: A005811.

Links

Antti Karttunen, The first 141 antidiagonals of the table, flattened

Formula

A(n,0) = A136480(n), n>0.

Example

The top-left corner of the array:
0, 0, 0, 0, 0, ... (0, in binary 0, has no runs (by convention), thus at first we have all-0 sequence)
1, 0, 0, 0, 0, ... (1, in binary 1, has one run of length 1)
1, 1, 0, 0, 0, ... (2, in binary 10, has two runs of length 1 both)
2, 0, 0, 0, 0, ... (3, in binary 11, has one run of length 2)
2, 1, 0, 0, 0, ... (4, in binary 100, the rightmost run of length 2 given first, then the second run of length 1)
1, 1, 1, 0, 0, ... (5, in binary 101, has three runs of one bit each)
1, 2, 0, 0, 0, ...
3, 0, 0, 0, 0, ...
3, 1, 0, 0, 0, ...
1, 2, 1, 0, 0, ...
1, 1, 1, 1, 0, ...
2, 1, 1, 0, 0, ...
2, 2, 0, 0, 0, ...
1, 1, 2, 0, 0, ...
1, 3, 0, 0, 0, ...
4, 0, 0, 0, 0, ...

Maple

A227186 := proc(n, k)
    local bdgs, ru, i, b, a;
    bdgs := convert(n, base, 2) ;
    if nops(bdgs) = 0 then
        return 0 ;
    end if;
    ru := 0 ;
    i := 1 ;
    b := op(i, bdgs) ;
    a := 1 ;
    for i from 2 to nops(bdgs) do
        if op(i, bdgs) <> op(i-1, bdgs) then
            if ru = k then
                return a;
            end if;
            a := 1 ;
            ru := ru+1 ;
        else
            a := a+1 ;
        end if;
    end do:
    if ru =k then
        a ;
    else
        0 ;
    end if;
end proc: # R. J. Mathar, Jul 23 2013

Prog

(Scheme)
(define (A227186 n) (A227186bi (A002262 n) (A025581 n)))
(define (A227186bi n k) (cond ((< (A005811 n) (+ 1 k)) 0) ((zero? k) (A136480 n)) (else (A227186bi (A163575 n) (- k 1)))))
(PARI) A227186(n, k)=while(k>=0, for(c=1, n, bittest(n, 0)==bittest(n\=2, 0)&next; k&break; return(c)); n||return; k--) \\ To let A(0, 0)=1 add "!n||!" in front of while(...). TO DO: add default value k=-1 and implement "flattened" sequence, such that A227186(n) yields a(n). _M. Hasler_, Jul 21 2013

Crossrefs

Used to compute A227183. Cf. also A163575, A227188, A227189.

Sequence in context: A187081 A369308 A212434 * A037134 A254612 A363886

Adjacent sequences: A227183 A227184 A227185 * A227187 A227188 A227189

Keyword

nonn,tabl,base

Author

Antti Karttunen, Jul 06 2013

Status

approved