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A265705 Triangle read by rows: T(n,k) = k IMPL n, 0 <= k <= n, bitwise logical IMPL. 13
0, 1, 1, 3, 2, 3, 3, 3, 3, 3, 7, 6, 5, 4, 7, 7, 7, 5, 5, 7, 7, 7, 6, 7, 6, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 15, 14, 13, 12, 11, 10, 9, 8, 15, 15, 15, 13, 13, 11, 11, 9, 9, 15, 15, 15, 14, 15, 14, 11, 10, 11, 10, 15, 14, 15, 15, 15, 15, 15, 11, 11, 11, 11, 15 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

T(n,0) = T(n,n) = A003817(n);

T(2*n,n) = A265716(n);

let m = A089633(n): T(m,k) = T(m,m-k), k = 0..m;

let m = A158582(n): T(m,k) != T(m,m-k) for at least one k <= a(n);

A265705(2*a(n),a(n)) = 2*a(n);

let m = A247648(n): T(2*m,m) = 2*m;

for n > 0: A029578(n+2) = number of odd terms in row n; no even terms in odd indexed rows.

A265885(n) = A265705(A000040(n),n);

A053644(n) = smallest k such that row k contains n.

LINKS

Reinhard Zumkeller, Rows n = 0..255 of triangle, flattened

Eric Weisstein's World of Mathematics, Implies

EXAMPLE

.          10 | 1010                            12 | 1100

.           4 |  100                             6 |  110

.   ----------+-----                     ----------+-----

.   4 IMPL 10 | 1011 -> T(12,6)=13       6 IMPL 12 | 1101 -> T(12,6)=13

.

First 16 rows of the triangle, where non-symmetrical rows are marked, see comment concerning A158582 and A089633:

.   0:                                 0

.   1:                               1   1

.   2:                             3   2   3

.   3:                           3   3   3   3

.   4:                         7   6   5   4   7    X

.   5:                       7   7   5   5   7   7

.   6:                     7   6   7   6   7   6   7

.   7:                   7   7   7   7   7   7   7   7

.   8:                15  14  13  12  11  10   9   8  15    X

.   9:              15  15  13  13  11  11   9   9  15  15    X

.  10:            15  14  15  14  11  10  11  10  15  14  15    X

.  11:          15  15  15  15  11  11  11  11  15  15  15  15

.  12:        15  14  13  12  15  14  13  12  15  14  13  12  15    X

.  13:      15  15  13  13  15  15  13  13  15  15  13  13  15  15

.  14:    15  14  15  14  15  14  15  14  15  14  15  14  15  14  15

.  15:  15  15  15  15  15  15  15  15  15  15  15  15  15  15  15  15 .

PROG

(Haskell)

a265705_tabl = map a265705_row [0..]

a265705_row n = map (a265705 n) [0..n]

a265705 n k = k `bimpl` n where

   bimpl 0 0 = 0

   bimpl p q = 2 * bimpl p' q' + if u <= v then 1 else 0

               where (p', u) = divMod p 2; (q', v) = divMod q 2

CROSSREFS

Cf. A003817, A007088, A029578, A051933 (XOR), A080098 (OR), A080099 (AND), A089633, A158582, A247648, A265716 (central terms), A265736 (row sums).

Cf. A053644, A265885.

Sequence in context: A079790 A098726 A065801 * A205237 A086920 A182021

Adjacent sequences:  A265702 A265703 A265704 * A265706 A265707 A265708

KEYWORD

nonn,tabl,look

AUTHOR

Reinhard Zumkeller, Dec 15 2015

STATUS

approved

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Last modified February 21 04:18 EST 2019. Contains 320371 sequences. (Running on oeis4.)