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A164874
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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).
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7
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2, 5, 6, 11, 13, 14, 23, 27, 29, 30, 47, 55, 59, 61, 62, 95, 111, 119, 123, 125, 126, 191, 223, 239, 247, 251, 253, 254, 383, 447, 479, 495, 503, 507, 509, 510, 767, 895, 959, 991, 1007, 1015, 1019, 1021, 1022, 1535, 1791, 1919, 1983, 2015, 2031, 2039, 2043
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OFFSET
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1,1
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COMMENTS
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T(n,k) = A030130(n*(n-1)/2 + k + 1);
A023416(T(n,k)) = 1, 1<=k<=n;
A059673(n) = sum of n-th row;
T(n,1) = A055010(n);
T(n,2) = A086224(n-2) for n > 1;
T(n,n-1) = A036563(n+1) for n > 1;
T(n,n) = A000918(n+1).
All terms contain exactly 1 zero in binary representation.
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LINKS
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Reinhard Zumkeller, Rows n = 1..100 of triangle, flattened
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FORMULA
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T(n,k) = 2^(n+1) - 2^(n-k) - 1, 1 <= k <= n.
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EXAMPLE
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Initial rows:
. 1: 2
. 2: 5 6
. 3: 11 13 14
. 4: 23 27 29 30
. 5: 47 55 59 61 62
. 6: 95 111 119 123 125 126
also in binary representation:
. 10
. 101 110
. 1011 1101 1110
. 10111 11011 11101 11110
. 101111 110111 111011 111101 111110
. 1011111 1101111 1110111 1111011 1111101 1111110 .
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PROG
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(Haskell)
a164874 n k = a164874_tabl !! (n-1) !! (k-1)
a164874_row n = a164874_tabl !! (n-1)
a164874_tabl = map reverse $ iterate f [2] where
f xs@(x:_) = (2 * x + 2) : map ((+ 1) . (* 2)) xs
-- Reinhard Zumkeller, Mar 31 2015
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CROSSREFS
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Cf. A030130, A023416, A059673, A055010, A086224, A036563, A000918.
Sequence in context: A140144 A328893 A030130 * A337498 A045845 A002133
Adjacent sequences: A164871 A164872 A164873 * A164875 A164876 A164877
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KEYWORD
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nonn,tabl
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AUTHOR
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Reinhard Zumkeller, Aug 29 2009
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STATUS
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approved
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