A267090 Triangle read by rows: Fill an n X n square with 1's, except for 0's on the two main diagonals. Then T(n,k) is decimal equivalent of the k-th row (0<=k<=n).

0, 0, 0, 2, 5, 2, 6, 9, 9, 6, 14, 21, 27, 21, 14, 30, 45, 51, 51, 45, 30, 62, 93, 107, 119, 107, 93, 62, 126, 189, 219, 231, 231, 219, 189, 126, 254, 381, 443, 471, 495, 471, 443, 381, 254, 510, 765, 891, 951, 975, 975, 951, 891, 765, 510

Offset

0,4

Comments

Inspired by A137932 and A042948.

Conjectures:

(i) The first column is A000225/2.

(ii) For even-n, T(n,n/2) = A129868.

(iii) For odd-n, T(n,(n-1)/2) = T(n,(n+1)/2) = A220236.

Links

Table of n, a(n) for n=0..54.

Kival Ngaokrajang, Illustration of initial terms, T(n,k) for n = 0..10, k = 0..10

Example

Triangle begins:
n\k  0   1   2   3   4   5   6   7   8 ...
0    0
1    0   0
2    2   5   2
3    6   9   9   6
4   14  21  27  21  14
5   30  45  51  51  45  30
6   62  93 107 119 107  93  62
7  126 189 219 231 231 219 189 126
8  254 381 443 471 495 471 443 381 254
...

Prog

(Small Basic)
t[0][0] = 1
t[1][0] = 3
t[1][1] = 3
TextWindow.Write("0, 0, 0, ")
For n = 2 To 20
  For k = 0 To n
    If k = 0 Or k = n then
      t[n][k] = 1 + math.Power(2, n)
    Else
      t[n][k] = 2*t[n-2][k-1]
    EndIf
    a = math.Power(2, n+1) -1 -t[n][k]
    TextWindow.Write(a+", ")
  EndFor
Endfor

Crossrefs

Cf. A000225, A042948, A129868, A137932, A267089.

Sequence in context: A242403 A179015 A195621 * A067948 A142148 A142583

Adjacent sequences: A267087 A267088 A267089 * A267091 A267092 A267093

Keyword

tabl,nonn

Author

Kival Ngaokrajang, Jan 10 2016

Status

approved