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%I #26 Dec 18 2020 04:07:29
%S 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,
%T 64,32,0,1093,728,484,320,208,128,64,0,3280,2186,1456,968,640,416,256,
%U 128,0,9841,6560,4372,2912,1936,1280,832,512,256,0
%N Rectangular array, a(m,n) = 2^(m-1)*(3^n-1), read by antidiagonals.
%C 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.
%C a(m,n) is independent of the number of zeros in the ternary expansion of the row number.
%C a(m,n) gives a non-recursive formula for A227428.
%H Marcus Jaiclin, et al. <a href="https://web.archive.org/web/20170823000349/http://pyrrho.wsc.ma.edu/math/faculty/jaiclin/writings/research/pascals_triangle/">Pascal's Triangle, Mod 2,3,5</a>
%e Initial 5 X 5 block of array (upper left corner is (0,0), row index m, column index n):
%e 0 1 4 13 40
%e 0 2 8 26 80
%e 0 4 16 52 160
%e 0 8 32 104 320
%e 0 16 64 208 640
%e Pascal's Triangle (mod 3), row numbers in ternary:
%e 1 <= Row 0, m=0, n=0, 2^(-1)(3^0-1) = #2's = 0
%e 1 1 <= Row 1, m=1, n=0, 2^0(3^0-1) = #2's = 0
%e 1 2 1 <= Row 2, m=0, n=1, 2^(-1)(3^1-1) = #2's = 1
%e 1 0 0 1 <= Row 10, m=1, n=0, 2^0(3^0-1) = #2's = 0
%e 1 1 0 1 1 <= Row 11, m=2, n=0, 2^1(3^0-1) = #2's = 0
%e 1 2 1 1 2 1 <= Row 12, m=1, n=1, 2^0(3^1-1) = #2's = 2
%e 1 0 0 2 0 0 1 <= Row 20, m=0, n=1, 2^(-1)(3^1-1) = #2's = 1
%e 1 1 0 2 2 0 1 1 <= Row 21, m=1, n=1, 2^0(3^1-1) = #2's = 2
%e 1 2 1 2 1 2 1 2 1 <= Row 22, m=0, n=2, 2^(-1)(3^2-1) = #2's = 4
%e 1 0 0 0 0 0 0 0 0 1 <= Row 100, m=1, n=0, 2^0(3^0-1) = #2's = 0
%Y Cf. A206427, A206424, A227428, A083093, A077267, A062756, A081603.
%Y Cf. A062296, A006047, A007318.
%K nonn,tabl,easy
%O 0,4
%A _Marcus Jaiclin_, Feb 07 2012
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