|
Search: id:A117939
|
|
|
| A117939 |
|
Triangle related to powers of 3 partitions of n. |
|
+0
8
|
|
| 1, 2, 1, 1, -2, 1, 2, 0, 0, 1, 4, 2, 0, 2, 1, 2, -4, 2, 1, -2, 1, 1, 0, 0, -2, 0, 0, 1, 2, 1, 0, -4, -2, 0, 2, 1, 1, -2, 1, -2, 4, -2, 1, -2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 2, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, -4, 2, 0, 0, 0, 0, 0, 0, 1, -2, 1, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 1, 8, 4, 0, 4, 2, 0, 0, 0, 0, 4, 2, 0, 2, 1, 4, -8, 4, 2, -4, 2
(list; table; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
A117939 mod 2=A117944. Row sums are A117940. Inverse is A117941. First column is A059151. Second column is A117946.
|
|
FORMULA
|
Triangle T(n,k)=sum{j=0..n, L(C(n,j)/3)*L(C(n-j,k)/3)} where L(j/p) is the Legendre symbol of j and p.
Matrix square of triangle A117947. Matrix log is the integer triangle A120854. - Paul D. Hanna (pauldhanna(AT)juno.com), Jul 08 2006
|
|
EXAMPLE
|
Triangle begins
1,
2, 1,
1, -2, 1,
2, 0, 0, 1,
4, 2, 0, 2, 1,
2, -4, 2, 1, -2, 1,
1, 0, 0, -2, 0, 0, 1,
2, 1, 0, -4, -2, 0, 2, 1,
1, -2, 1, -2, 4, -2, 1, -2, 1
|
|
PROGRAM
|
(PARI) {T(n, k)=(matrix(n+1, n+1, r, c, (binomial(r-1, c-1)+1)%3-1)^2)[n+1, k+1]} - Paul D. Hanna (pauldhanna(AT)juno.com), Jul 08 2006
|
|
CROSSREFS
|
Cf. A120854 (matrix log), A117947 (matrix square-root).
Sequence in context: A133009 A053734 A057856 this_sequence A105522 A131774 A078316
Adjacent sequences: A117936 A117937 A117938 this_sequence A117940 A117941 A117942
|
|
KEYWORD
|
easy,sign,tabl
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), Apr 05 2006
|
|
|
Search completed in 0.002 seconds
|
