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A081118
Triangle of first n numbers per row having exactly n 1's in binary representation.
10
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
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
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
KEYWORD
nonn,tabl
AUTHOR
Reinhard Zumkeller, Mar 06 2003
STATUS
approved