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A206428
Rectangular array, a(m,n) = 2^(m-1)*(3^n-1), read by antidiagonals.
2
0, 1, 0, 4, 2, 0, 13, 8, 4, 0, 40, 26, 16, 8, 0, 121, 80, 52, 32, 16, 0, 364, 242, 160, 104, 64, 32, 0, 1093, 728, 484, 320, 208, 128, 64, 0, 3280, 2186, 1456, 968, 640, 416, 256, 128, 0, 9841, 6560, 4372, 2912, 1936, 1280, 832, 512, 256, 0
OFFSET
0,4
COMMENTS
Number of 2's in any row of Pascal's triangle (mod 3) whose row number has exactly m 1's and n 2's in its ternary expansion.
a(m,n) is independent of the number of zeros in the ternary expansion of the row number.
a(m,n) gives a non-recursive formula for A227428.
EXAMPLE
Initial 5 X 5 block of array (upper left corner is (0,0), row index m, column index n):
0 1 4 13 40
0 2 8 26 80
0 4 16 52 160
0 8 32 104 320
0 16 64 208 640
Pascal's Triangle (mod 3), row numbers in ternary:
1 <= Row 0, m=0, n=0, 2^(-1)(3^0-1) = #2's = 0
1 1 <= Row 1, m=1, n=0, 2^0(3^0-1) = #2's = 0
1 2 1 <= Row 2, m=0, n=1, 2^(-1)(3^1-1) = #2's = 1
1 0 0 1 <= Row 10, m=1, n=0, 2^0(3^0-1) = #2's = 0
1 1 0 1 1 <= Row 11, m=2, n=0, 2^1(3^0-1) = #2's = 0
1 2 1 1 2 1 <= Row 12, m=1, n=1, 2^0(3^1-1) = #2's = 2
1 0 0 2 0 0 1 <= Row 20, m=0, n=1, 2^(-1)(3^1-1) = #2's = 1
1 1 0 2 2 0 1 1 <= Row 21, m=1, n=1, 2^0(3^1-1) = #2's = 2
1 2 1 2 1 2 1 2 1 <= Row 22, m=0, n=2, 2^(-1)(3^2-1) = #2's = 4
1 0 0 0 0 0 0 0 0 1 <= Row 100, m=1, n=0, 2^0(3^0-1) = #2's = 0
KEYWORD
nonn,tabl,easy
AUTHOR
Marcus Jaiclin, Feb 07 2012
STATUS
approved