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

Author

Alois P. Heinz, Sep 04 2014

Keywords

• nonn
• tabl
• base
• look
• nice

Examples

			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
		

Links

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

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).

Programs

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

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 *)

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