A062177 Shifts left when MASKCONVolved with itself.

1, 1, 2, 4, 12, 24, 72, 192, 720, 1440, 4320, 11520, 43200, 103680, 362880, 1105920, 4665600, 9331200, 27993600, 74649600, 279936000, 671846400, 2351462400, 7166361600, 30233088000, 67184640000, 221709312000, 644972544000

Offset: 0

Author

Antti Karttunen, Jun 12 2001

Keywords

• nonn
• eigen

Comments

Note that the factorials 1!, 2!, 4!, 6!, 9! can be found from the positions 1,3,6,9,15 (or 2,4,7,10,16 if zero-based indexing is used) of this sequence. I do not know whether any larger factorials occur in the sequence.

Links

• N. J. A. Sloane, Transforms

Crossrefs

Other self-convolved sequences: A000108, A007460 - A007464, A025192, A038044, A061922.

Programs

Maple

EIGENbyMASKCONV := proc(upto_n) local n,a,j,i,s,m; a := [1]; for i from 0 to upto_n do s := 0; m := maskees(i); n := nops(m); for j from 1 to n do s := s+(a[m[j]+1]*a[m[(n-j)+1]+1]); od; a := [op(a),s]; od; RETURN(a); end;
maskees := proc(n) local a,b,u,i; a := []; b := list_mask_bits(n); u := (2^nops(b))-1; for i from 0 to u do a := [op(a),sum_by_mask_list(i,b)]; od; RETURN(a); end;
list_mask_bits := proc(nn) local n,a,x; n := nn; x := 1; a := []; while(n > 0) do if(1 = (n mod 2)) then a := [op(a),x]; fi; n := floor(n/2); x := 2*x; od; RETURN(a); end;
sum_by_mask_list := proc(nn,a) local n,i,s; n := nn; s := 0; i := 1; while(n > 0) do if(1 = (n mod 2)) then s := s + a[i]; fi; n := floor(n/2); i := i+1; od; RETURN(s); end;