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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.
5
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
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
KEYWORD
nonn,tabl,base,look,nice
AUTHOR
Alois P. Heinz, Sep 04 2014
STATUS
approved