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A379147 Irregular triangle T(n, k), n >= 0, k = 1..2^A007895(n), read by rows; the n-th row lists the integers m such that A184617(abs(m)) = A003714(n).

%I A379147 #9 Dec 20 2024 12:36:57
%S A379147 0,-1,1,-2,2,-4,4,-5,-3,3,5,-8,8,-9,-7,7,9,-10,-6,6,10,-16,16,-17,-15,
%T A379147 15,17,-18,-14,14,18,-20,-12,12,20,-21,-19,-13,-11,11,13,19,21,-32,32,
%U A379147 -33,-31,31,33,-34,-30,30,34,-36,-28,28,36
%N A379147 Irregular triangle T(n, k), n >= 0, k = 1..2^A007895(n), read by rows; the n-th row lists the integers m such that A184617(abs(m)) = A003714(n).
%C A379147 A permutation of the integers (Z).
%C A379147 For any n >= 0:
%C A379147 - in the Zeckendorf expansion of n,
%C A379147 - replace each Fibonacci number, say A000045(2+i) with i >= 0, by 2^i or -2^i,
%C A379147 - the various values obtained make up the n-th row.
%H A379147 Rémy Sigrist, <a href="/A379147/b379147.txt">Table of n, a(n) for n = 0..10922</a> (rows for n = 0..609 flattened)
%H A379147 <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>
%F A379147 T(n, 1) = -A003714(n).
%F A379147 T(n, 2^A007895(n)) = A003714(n).
%F A379147 T(n, k) = -T(n, 2^A007895(n)+1-k) for k = 1..2^A007895(n).
%e A379147 Triangle T(n, k) begins:
%e A379147   n   n-th row
%e A379147   --  ----------------------------------
%e A379147    0  0
%e A379147    1  -1, 1
%e A379147    2  -2, 2
%e A379147    3  -4, 4
%e A379147    4  -5, -3, 3, 5
%e A379147    5  -8, 8
%e A379147    6  -9, -7, 7, 9
%e A379147    7  -10, -6, 6, 10
%e A379147    8  -16, 16
%e A379147    9  -17, -15, 15, 17
%e A379147   10  -18, -14, 14, 18
%e A379147   11  -20, -12, 12, 20
%e A379147   12  -21, -19, -13, -11, 11, 13, 19, 21
%e A379147   13  -32, 32
%e A379147   14  -33, -31, 31, 33
%e A379147   15  -34, -30, 30, 34
%o A379147 (PARI) tozeck(n) = { for (i=0, oo, if (n<=fibonacci(2+i), my (v=0, f); forstep (j=i, 0, -1, if (n>=f=fibonacci(2+j), n-=f; v+=2^j;); if (n==0, return (v););););); }
%o A379147 row(n) = { my (z = tozeck(n), r = [0], b); while (z, z -= b = 2^valuation(z, 2); r = concat([v - b | v <- r], [v + b | v <- r]);); return (r); }
%Y A379147 Cf. A000045, A003714, A007895, A184617, A379175.
%K A379147 sign,tabf,base
%O A379147 0,4
%A A379147 _Rémy Sigrist_, Dec 16 2024