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A062177
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Shifts left when MASKCONVolved with itself.
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2
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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
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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MAPLE
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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;
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CROSSREFS
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KEYWORD
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nonn,eigen
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AUTHOR
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Antti Karttunen, Jun 12 2001
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STATUS
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approved
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