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A117939 Triangle related to powers of 3 partitions of n. 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; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A117939 mod 2=A117944. Row sums are A117940. Inverse is A117941. First column is A059151. Second column is A117946.

LINKS

Table of n, a(n) for n=0..110.

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, 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

PROG

(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, Jul 08 2006

CROSSREFS

Cf. A120854 (matrix log), A117947 (matrix square-root).

Sequence in context: A214501 A318665 A057856 * A276167 A105522 A131774

Adjacent sequences:  A117936 A117937 A117938 * A117940 A117941 A117942

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Apr 05 2006

STATUS

approved

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Last modified October 20 15:22 EDT 2018. Contains 316388 sequences. (Running on oeis4.)