login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; table; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 20 04:12 EST 2020. Contains 332063 sequences. (Running on oeis4.)