OFFSET
0,2
COMMENTS
Rectangular array giving the number of 1'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 (listed by antidiagonals).
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 A206424.
LINKS
Marcus Jaiclin, et al. Pascal's Triangle, Mod 2,3,5
FORMULA
a(m, n) = 2^(m - 1)(3^n + 1).
EXAMPLE
Initial 5 X 5 block of entries (upper corner is (m,n)=(0,0), m increases down, n increases across):
1 2 5 14 41
2 4 10 28 82
4 8 20 56 164
8 16 40 112 328
16 32 80 224 656
Pascal's Triangle (mod 3), row numbers in ternary:
1 <= Row 0, m = 0, n = 0, 2^(-1)(3^0 + 1) = #1's = 1
1 1 <= Row 1, m = 1, n = 0, 2^0(3^0 + 1) = #1's = 2
1 2 1 <= Row 2, m = 0, n = 1, 2^(-1)(3^1 + 1) = #1's = 2
1 0 0 1 <= Row 10, m = 1, n = 0, 2^0(3^0 + 1) = #1's = 2
1 1 0 1 1 <= Row 11, m = 2, n = 0, 2^1(3^0 + 1) = #1's = 4
1 2 1 1 2 1 <= Row 12, m = 1, n = 1, 2^0(3^1 + 1) = #1's = 4
1 0 0 2 0 0 1 <= Row 20, m = 0, n = 1, 2^(-1)(3^1 + 1) = #1's = 2
1 1 0 2 2 0 1 1 <= Row 21, m = 1, n = 1, 2^0(3^1 + 1) = #1's = 4
1 2 1 2 1 2 1 2 1 <= Row 22, m = 0, n = 2, 2^(-1)(3^2 + 1) = #1's = 5
1 0 0 0 0 0 0 0 0 1 <= Row 100, m = 1, n = 0, 2^0(3^0 + 1) = #1's = 2
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Marcus Jaiclin, Feb 07 2012
STATUS
approved