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 A163233 Two-dimensional Binary Reflected Gray Code: a(i,j) = bits of binary expansion of A003188(i) interleaved with that of A003188(j). 7
 0, 1, 2, 5, 3, 10, 4, 7, 11, 8, 20, 6, 15, 9, 40, 21, 22, 14, 13, 41, 42, 17, 23, 30, 12, 45, 43, 34, 16, 19, 31, 28, 44, 47, 35, 32, 80, 18, 27, 29, 60, 46, 39, 33, 160, 81, 82, 26, 25, 61, 62, 38, 37, 161, 162, 85, 83, 90, 24, 57, 63, 54, 36, 165, 163, 170, 84, 87, 91 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The top left 8 X 8 corner of the array is +0 +1 +5 +4 20 21 17 16 +2 +3 +7 +6 22 23 19 18 10 11 15 14 30 31 27 26 +8 +9 13 12 28 29 25 24 40 41 45 44 60 61 57 56 42 43 47 46 62 63 59 58 34 35 39 38 54 55 51 50 32 33 37 36 52 53 49 48 By taking the top left 2 X 2 corner, 2 X 4 rectangle ((0,1,5,4),(2,3,7,6)) or 4 X 4 corner one obtains Karnaugh map templates for 2, 3 or 4 variables respectively (although not the standard ones usually given in the textbooks). LINKS A. Karttunen, Table of n, a(n) for n = 0..2079 Wikipedia, Karnaugh map FORMULA a(x,y) = A000695(A003188(x)) + 2*A000695(A003188(y)). MATHEMATICA Table[Function[k, FromDigits[#, 2] &@ Apply[Function[{a, b}, Riffle @@ Map[PadLeft[#, Max[Length /@ {a, b}]] &, {a, b}]], Map[IntegerDigits[#, 2] &@ BitXor[#, Floor[#/2]] &, {k, j}]]][i - j], {i, 0, 11}, {j, i, 0, -1}] // Flatten (* Michael De Vlieger, Jun 25 2017 *) PROG (Scheme:) (define (A163233bi x y) (+ (A000695 (A003188 x)) (* 2 (A000695 (A003188 y))))) (define (A163233 n) (A163233bi (A025581 n) (A002262 n))) (Python) def a000695(n):     n=bin(n)[2:]     x=len(n)     return sum([int(n[i])*4**(x - 1 - i) for i in xrange(x)]) def a003188(n): return n^(n>>1) def a(n, k): return a000695(a003188(n)) + 2*a000695(a003188(k)) for n in xrange(21): print [a(n - k, k) for k in xrange(n + 1)] # Indranil Ghosh, Jun 25 2017 CROSSREFS Inverse: A163234. a(n) = A057300(A163235(n)). Transpose: A163235. Row sums: A163242. Cf. A054238, A147995. Sequence in context: A044043 A133128 A057337 * A096666 A191855 A064664 Adjacent sequences:  A163230 A163231 A163232 * A163234 A163235 A163236 KEYWORD nonn,tabl AUTHOR Antti Karttunen, Jul 29 2009 STATUS approved

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