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A158565
A modulo two based Pascal's triangle using powers of two for even and powers of three for odd: t(n,m)=If[Mod[Binomial[n, m], 2] == 0 && m <= Floor[n/2], 2^m, If[Mod[Binomial[n, m], 2] == 0 && m > Floor[n/2], 2^(n - m), If[Mod[Binomial[n, m], 2] == 1 && m <= Floor[n/2], 3^m, If[Mod[Binomial[n, m], 2] == 1 && m > Floor[n/2], 3^(n - m), 0]]]].
0
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 4, 2, 1, 1, 3, 4, 4, 3, 1, 1, 2, 9, 8, 9, 2, 1, 1, 3, 9, 27, 27, 9, 3, 1, 1, 2, 4, 8, 16, 8, 4, 2, 1, 1, 3, 4, 8, 16, 16, 8, 4, 3, 1, 1, 2, 9, 8, 16, 32, 16, 8, 9, 2, 1
OFFSET
0,5
COMMENTS
Row sums are:
{1, 2, 4, 8, 10, 16, 32, 80, 46, 64, 104,...}.
FORMULA
t(n,m)=If[Mod[Binomial[n, m], 2] == 0 && m <= Floor[n/2], 2^m,
If[Mod[Binomial[n, m], 2] == 0 && m > Floor[n/2], 2^(n - m),
If[Mod[Binomial[n, m], 2] == 1 && m <= Floor[n/2], 3^m,
If[Mod[Binomial[n, m], 2] == 1 && m > Floor[n/2], 3^(n - m), 0]]]].
EXAMPLE
{1},
{1, 1},
{1, 2, 1},
{1, 3, 3, 1},
{1, 2, 4, 2, 1},
{1, 3, 4, 4, 3, 1},
{1, 2, 9, 8, 9, 2, 1},
{1, 3, 9, 27, 27, 9, 3, 1},
{1, 2, 4, 8, 16, 8, 4, 2, 1},
{1, 3, 4, 8, 16, 16, 8, 4, 3, 1},
{1, 2, 9, 8, 16, 32, 16, 8, 9, 2, 1}
MATHEMATICA
Table[Table[If[Mod[Binomial[n, m], 2] == 0 && m <= Floor[n/2], 2^m,
If[Mod[Binomial[n, m], 2] == 0 && m > Floor[n/2], 2^(n - m),
If[Mod[Binomial[n, m], 2] == 1 && m <= Floor[n/2], 3^m,
If[Mod[Binomial[n, m], 2] == 1 && m > Floor[n/2], 3^(n - m),
0]]]], {m, 0, n}], {n, 0, 10}];
Flatten[%]
CROSSREFS
Sequence in context: A093557 A098802 A048804 * A132422 A065133 A343033
KEYWORD
nonn,tabl,uned
AUTHOR
Roger L. Bagula, Mar 21 2009
STATUS
approved