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".

1, 2, 9, 150, 38505, 2523490710, 10838310072981296745, 199931532107794273605284333428918544790, 68033174967769840440887906939858451149105560803546820641877549596291376780905

Offset: 0

Author

Dan Reif (integer-sequences(AT)angelfaq.com), Nov 28 2007, corrected Nov 30 2007

Keywords

• nonn
• base

Comments

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

Crossrefs

Cf. A080814, A080815, A048707.

Programs

Mathematica

FromDigits[#, 2] & /@ NestList[ Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {1}, 9] (* Robert G. Wilson v, Aug 16 2011 *)

Pseudocode

function invert(string s) returns string { s.replace("0","2"); s.replace("1","0"); s.replace("2","1"); }
function f(int n) returns string { if (n==0) return "1"; return concat(f(n-1),invert(f(n-1))); } // Blatant opportunity for optimization
function a(int n) returns int { return f(n).InterpretAsBinary(); }

Formula

The "~" operator, as used here, represents bitwise complement. a(0) = 1. a(n) = a(n-1) followed by ~a(n-1).