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A260211
Irregular triangle read by rows, T(n,k) is the decimal number conversion from an n-bit symmetric binary table arranged in ascending order for n > 1.
1
0, 1, 0, 3, 0, 2, 5, 7, 0, 6, 9, 15, 0, 4, 10, 14, 17, 21, 27, 31, 0, 12, 18, 30, 33, 45, 51, 63, 0, 8, 20, 28, 34, 42, 54, 62, 65, 73, 85, 93, 99, 107, 119, 127, 0, 24, 36, 60, 66, 90, 102, 126, 129, 153, 165, 189, 195, 219, 231, 255
OFFSET
1,4
COMMENTS
The sequence of row lengths is A060546(n).
Column 2 is A164073. See illustration.
EXAMPLE
The irregular triangle begins:
n\k 0 1 2 3 4 5 6 7 ...
1 0 1
2 0 3
3 0 2 5 7
4 0 6 9 15
5 0 4 10 14 17 21 27 31
6 0 12 18 30 33 45 51 63
...
MATHEMATICA
Flatten[Table[Select[Range[0, 2^k -1], #==IntegerReverse[#, 2, k]&], {k, 1, 8}]] (* Ed Pegg Jr, May 03 2021 *)
PROG
(Small Basic)
For n=1 To 10
j=1
c1=math.Power(-1, n)
c2=((5+c1)*math.Power(2, 1/4*(2*n-1+c1)))/4
row=math.power(2, Math.Ceiling(n/2))
For k = 0 To row-1
If k=0 then
a[n][k]=0
EndIf
If k=1 Then
a[n][k]=c2
EndIf
If k>1 And k<row/2 Then
a[n][k]=2*a[n-2][k]
EndIf
If k=row/2 Then
a[n][k]=a[n][k-1]+3
EndIf
If k>row/2 And k<row-1 Then
a[n][k]=a[n][k-1]+a[n][j]-a[n][j-1]
j=j+1
EndIf
If k=row-1 Then
a[n][k]=math.Power(2, n)-1
endif
TextWindow.Write(a[n][k]+", ")
EndFor
EndFor
CROSSREFS
Sequence in context: A089598 A117139 A159959 * A255008 A222602 A058544
KEYWORD
nonn,easy,tabf
AUTHOR
Kival Ngaokrajang, Jul 19 2015
STATUS
approved