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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 (list; table; graph; refs; listen; history; text; internal format)
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.

LINKS

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

Marcus Jaiclin, et al. Pascal's Triangle Mod 2,3,5

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

CROSSREFS

Cf. A206427, A206424, A227428, A083093, A077267, A062756, A081603.

Cf. A062296, A006047, A007318.

Sequence in context: A091435 A118441 A244131 * A111549 A279411 A022696

Adjacent sequences:  A206425 A206426 A206427 * A206429 A206430 A206431

KEYWORD

nonn,tabl,easy

AUTHOR

Marcus Jaiclin, Feb 07 2012

STATUS

approved

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Last modified January 17 05:26 EST 2019. Contains 319207 sequences. (Running on oeis4.)