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A081118
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Triangle of first n numbers per row having exactly n 1's in binary representation.
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10
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1, 3, 5, 7, 11, 13, 15, 23, 27, 29, 31, 47, 55, 59, 61, 63, 95, 111, 119, 123, 125, 127, 191, 223, 239, 247, 251, 253, 255, 383, 447, 479, 495, 503, 507, 509, 511, 767, 895, 959, 991, 1007, 1015, 1019, 1021, 1023, 1535, 1791, 1919, 1983, 2015, 2031, 2039, 2043
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OFFSET
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1,2
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COMMENTS
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T(n,n) = A036563(n+1) = 2^(n+1) - 3.
Numbers of the form 2^t - 2^k - 1, 1 <= k < t.
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LINKS
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FORMULA
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T(n, k) = 2^(n+1) - 2^(n-k+1) - 1, 1<=k<=n.
a(n) = (2^A002260(n)-1)*2^A004736(n)-1; a(n)=(2^i-1)*2^j-1, where i=n-t*(t+1)/2, j=(t*t+3*t+4)/2-n, t=floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Apr 04 2013
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EXAMPLE
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Triangle begins:
.......... 1 ......... ................ 1
........ 3...5 ....... .............. 11 101
...... 7..11..13 ..... .......... 111 1011 1101
... 15..23..27..29 ... ...... 1111 10111 11011 11101
. 31..47..55..59..61 . . 11111 101111 110111 111011 111101.
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MATHEMATICA
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Table[2^(n+1)-2^(n-k+1)-1, {n, 10}, {k, n}]//Flatten (* Harvey P. Dale, Apr 09 2020 *)
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PROG
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(Haskell)
a081118 n k = a081118_tabl !! (n-1) !! (k-1)
a081118_row n = a081118_tabl !! (n-1)
a081118_tabl = iterate
(\row -> (map ((+ 1) . (* 2)) row) ++ [4 * (head row) + 1]) [1]
a081118_list = concat a081118_tabl
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CROSSREFS
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Cf. A000079, A018900, A014311, A014312, A014313, A023688, A023689, A023690, A023691, A038461, A038462, A038463.
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KEYWORD
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AUTHOR
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STATUS
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approved
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