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%I #5 Mar 31 2015 17:37:02
%S 2,5,6,11,13,14,23,27,29,30,47,55,59,61,62,95,111,119,123,125,126,191,
%T 223,239,247,251,253,254,383,447,479,495,503,507,509,510,767,895,959,
%U 991,1007,1015,1019,1021,1022,1535,1791,1919,1983,2015,2031,2039,2043
%N Triangle read by rows: T(1,1)=2; T(n,k)=2*T(n-1,k)+1, 1<=k<n; T(n,n)=2*(T(n-1,n-1)+1).
%C T(n,k) = A030130(n*(n-1)/2 + k + 1);
%C A023416(T(n,k)) = 1, 1<=k<=n;
%C A059673(n) = sum of n-th row;
%C T(n,1) = A055010(n);
%C T(n,2) = A086224(n-2) for n > 1;
%C T(n,n-1) = A036563(n+1) for n > 1;
%C T(n,n) = A000918(n+1).
%C All terms contain exactly 1 zero in binary representation.
%H Reinhard Zumkeller, <a href="/A164874/b164874.txt">Rows n = 1..100 of triangle, flattened</a>
%F T(n,k) = 2^(n+1) - 2^(n-k) - 1, 1 <= k <= n.
%e Initial rows:
%e . 1: 2
%e . 2: 5 6
%e . 3: 11 13 14
%e . 4: 23 27 29 30
%e . 5: 47 55 59 61 62
%e . 6: 95 111 119 123 125 126
%e also in binary representation:
%e . 10
%e . 101 110
%e . 1011 1101 1110
%e . 10111 11011 11101 11110
%e . 101111 110111 111011 111101 111110
%e . 1011111 1101111 1110111 1111011 1111101 1111110 .
%o (Haskell)
%o a164874 n k = a164874_tabl !! (n-1) !! (k-1)
%o a164874_row n = a164874_tabl !! (n-1)
%o a164874_tabl = map reverse $ iterate f [2] where
%o f xs@(x:_) = (2 * x + 2) : map ((+ 1) . (* 2)) xs
%o -- _Reinhard Zumkeller_, Mar 31 2015
%Y Cf. A030130, A023416, A059673, A055010, A086224, A036563, A000918.
%K nonn,tabl
%O 1,1
%A _Reinhard Zumkeller_, Aug 29 2009
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