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A133468 A080814 complemented, then interpreted as binary and then re-expressed in decimal form (e.g., "1221" = "0110"). Alternately, view as A080814 with "1" mapped to "1" and "2" mapped to "0".

%I A133468 #26 Sep 24 2024 09:21:04
%S A133468 1,2,9,150,38505,2523490710,10838310072981296745,
%T A133468 199931532107794273605284333428918544790,
%U A133468 68033174967769840440887906939858451149105560803546820641877549596291376780905
%N A133468 A080814 complemented, then interpreted as binary and then re-expressed in decimal form (e.g., "1221" = "0110"). Alternately, view as A080814 with "1" mapped to "1" and "2" mapped to "0".
%C A133468 It appears that a(n) is the least positive number with binary expansion Sum_{k = 0..w} b_k * 2^k such that the polynomial Sum_{k = 0..w} (X+k)^n * (-1)^b_k is constant. - _Rémy Sigrist_, Sep 15 2020
%F A133468 The "~" operator, as used here, represents bitwise complement. a(0) = 1. a(n) = a(n-1) followed by ~a(n-1).
%t A133468 FromDigits[#, 2] & /@ NestList[ Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {1}, 9] (* _Robert G. Wilson v_, Aug 16 2011 *)
%o A133468 (Pseudocode)
%o A133468 function invert(string s) returns string { s.replace("0","2"); s.replace("1","0"); s.replace("2","1"); }
%o A133468 function f(int n) returns string { if (n==0) return "1"; return concat(f(n-1),invert(f(n-1))); } // Blatant opportunity for optimization
%o A133468 function a(int n) returns int { return f(n).InterpretAsBinary(); }
%Y A133468 Cf. A080814, A080815, A048707.
%K A133468 nonn,base
%O A133468 0,2
%A A133468 Dan Reif (integer-sequences(AT)angelfaq.com), Nov 28 2007, corrected Nov 30 2007