A246830 T(n,k) is the concatenation of n-k and n+k in binary; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

0, 3, 2, 10, 7, 4, 15, 20, 13, 6, 36, 29, 22, 15, 8, 45, 38, 31, 40, 25, 10, 54, 47, 72, 57, 42, 27, 12, 63, 104, 89, 74, 59, 44, 29, 14, 136, 121, 106, 91, 76, 61, 46, 31, 16, 153, 138, 123, 108, 93, 78, 63, 80, 49, 18, 170, 155, 140, 125, 110, 95, 144, 113, 82, 51, 20

Offset

0,2

Links

Alois P. Heinz, Rows n = 0..127, flattened

Example

Triangle T(n,k) begins:
   0
   3  2
  10  7  4
  15 20 13  6
  36 29 22 15  8
  45 38 31 40 25 10
  54 47 72 57 42 27 12
Triangle T(n,k) written in binary (with | denoting the concat operation) begins:
     |0
    1|1      |10
   10|10    1|11     |100
   11|11   10|100   1|101    |110
  100|100  11|101  10|110   1|111    |1000
  101|101 100|110  11|111  10|1000  1|1001  |1010
  110|110 101|111 100|1000 11|1001 10|1010 1|1011 |1100

Maple

f:= proc(i, j) local r, h, k; r:=0; h:=0; k:=j;
      while k>0 do r:=r+2^h*irem(k, 2, 'k'); h:=h+1 od; k:=i;
      while k>0 do r:=r+2^h*irem(k, 2, 'k'); h:=h+1 od; r
    end:
T:= (n, k)-> f(n-k, n+k):
seq(seq(T(n, k), k=0..n), n=0..14);

Mathematica

f[i_, j_] := Module[{r, h, k, m}, r=0; h=0; k=j; While[k>0, {k, m} = QuotientRemainder[k, 2]; r = r+2^h*m; h = h+1]; k=i; While[k>0, {k, m} = QuotientRemainder[k, 2]; r = r+2^h*m; h = h+1]; r]; T[n_, k_] := f[n-k, n+k]; Table[Table[T[n, k], {k, 0, n}], {n, 0, 14}] // Flatten (* Jean-François Alcover, Oct 03 2016, adapted from Maple *)

Prog

(Haskell)
import Data.Function (on)
a246830 n k = a246830_tabl !! n !! k
a246830_row n = a246830_tabl !! n
a246830_tabl = zipWith (zipWith f) a051162_tabl a025581_tabl where
   f x y = foldr (\b v -> 2 * v + b) 0 $ x |+| y
   (|+|) = (++) `on` a030308_row
-- Reinhard Zumkeller, Sep 04 2014
(Python)
A246830 = []
for n in range(10**2):
....for k in range(n):
........A246830.append(int(bin(n-k)[2:]+bin(n+k)[2:], 2))
....A246830.append(2*n) # Chai Wah Wu, Sep 05 2014

Crossrefs

Column k=0 gives A020330.

T(n+1,n) gives A080565(n+1).

T(2n,n) gives A246831.

Main diagonal gives A005843.

Cf. A007088, A030308, A051162, A025581, A246520 (row maxima).

Sequence in context: A063549 A071653 A227631 * A268531 A056861 A302846

Adjacent sequences: A246827 A246828 A246829 * A246831 A246832 A246833

Keyword

nonn,tabl,base,look,nice

Author

Alois P. Heinz, Sep 04 2014

Status

approved