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 A081118 Triangle of first n numbers per row having exactly n 1's in binary representation. 9
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS T(n,n) = A036563(n+1) = 2^(n+1) - 3. Numbers of the form 2^t - 2^k - 1, 1 <= k < t. LINKS Reinhard Zumkeller, Rows n=1..150 of triangle, flattened FORMULA 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 EXAMPLE 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. MATHEMATICA Table[2^(n+1)-2^(n-k+1)-1, {n, 10}, {k, n}]//Flatten (* Harvey P. Dale, Apr 09 2020 *) PROG (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 -- Reinhard Zumkeller, Feb 23 2012 CROSSREFS Cf. A000079, A018900, A014311, A014312, A014313, A023688, A023689, A023690, A023691, A038461, A038462, A038463. Cf. A181741 (primes), A208083, subsequence of A089633. Cf. A131094. Sequence in context: A153183 A247648 A117203 * A003255 A263321 A244365 Adjacent sequences:  A081115 A081116 A081117 * A081119 A081120 A081121 KEYWORD nonn,tabl AUTHOR Reinhard Zumkeller, Mar 06 2003 STATUS approved

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Last modified January 21 12:45 EST 2021. Contains 340350 sequences. (Running on oeis4.)