A164874 - OEIS

A164874

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).

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

1,1

COMMENTS

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.

LINKS

Reinhard Zumkeller, Rows n = 1..100 of triangle, flattened

FORMULA

T(n,k) = 2^(n+1) - 2^(n-k) - 1, 1 <= k <= n.

EXAMPLE

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 .

PROG

(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

CROSSREFS

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

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Aug 29 2009

STATUS

approved