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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.

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 October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)