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A101211 Triangle read by rows: n-th row is length of run of leftmost 1's, followed by length of run of 0's, followed by length of run of 1's, etc., in the binary representation of n. 12
1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 3, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 3, 1, 4, 1, 4, 1, 3, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 3, 2, 2, 1, 2, 1, 1, 1, 2, 1, 2, 3, 2, 3, 1, 1, 4, 1, 5, 1, 5, 1, 4, 1, 1, 3, 1, 1, 1, 3, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row n has A005811(n) elements. In rows 2^(k-1)..2^k-1 we have all the compositions (ordered partitions) of k. Other orderings of compositions: A066099, A108244, and A124734. - Jason Kimberley, Feb 09 2013

A043276(n) = largest term in n-th row. - Reinhard Zumkeller, Dec 16 2013

LINKS

Antti Karttunen, The rows 1..1023 of the table, flattened

FORMULA

a(n) = A227736(A227741(n)) = A227186(A056539(A227737(n)),A227740(n)) - Antti Karttunen, Jul 27 2013

EXAMPLE

Since 9 is 1001 in binary, the 9th row is 1,2,1.

Since 11 is 1011 in binary, the 11th row is 1,1,2.

Triangle begins:

1;

1,1;

2;

1,2;

1,1,1;

2,1;

3;

1,3;

PROG

(Scheme, two variants)

(define (A101211 n) (A227736 (A227741 n)))

(define (A101211v2 n) (A227186bi (A056539 (A227737 n)) (A227740 n)))

;; Scheme-implementation for A227186bi can be found under A227186. - Antti Karttunen, Jul 27 2013

(Haskell)

import Data.List (group)

a101211 n k = a101211_tabf !! (n-1) !! (k-1)

a101211_row n = a101211_tabf !! (n-1)

a101211_tabf = map (reverse . map length . group) $ tail a030308_tabf

-- Reinhard Zumkeller, Dec 16 2013

CROSSREFS

A070939(n) gives the sum of terms in row n, while A167489(n) gives the product of its terms. A090996 gives the first column. A227736 lists the terms of each row in reverse order.

Cf. also A227186.

Cf. A030308, A175911.

Sequence in context: A245548 A025903 A175327 * A081652 A140816 A029433

Adjacent sequences:  A101208 A101209 A101210 * A101212 A101213 A101214

KEYWORD

nonn,tabf

AUTHOR

Leroy Quet, Dec 13 2004

EXTENSIONS

More terms from Emeric Deutsch, Apr 12 2005

STATUS

approved

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Last modified March 28 11:45 EDT 2017. Contains 284186 sequences.