A101309 - OEIS

A101309

Matrix logarithm of A047999 (Pascal's triangle mod 2).

0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0

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OFFSET

0,1

COMMENTS

Row sums equal A000120 (binary 1's-counting sequence). Antidiagonal sums form A101979.

LINKS

Table of n, a(n) for n=0..104.

FORMULA

T(n, k)=1 when n XOR k = 2^m for integer m>=0, T(n, k)=0 elsewhere.

EXAMPLE

T(n,k)=1 when n XOR k is a power of 2:

T(3,2)=1 since 3 XOR 2 = 2^0, T(4,0)=1 since 4 XOR 0 = 2^2,

T(5,1)=1 since 5 XOR 1 = 2^2, T(6,4)=1 since 6 XOR 4 = 2^2.

Rows begin:

[0],

[1, 0],

[1,0, 0],

[0,1, 1,0],

[1,0,0,0, 0],

[0,1,0,0, 1,0],

[0,0,1,0, 1,0,0],

[0,0,0,1, 0,1,1,0],...

PROG

(PARI) T(n, k)=if(n>k&bitxor(n, k)==2^valuation(bitxor(n, k), 2), 1, 0)

CROSSREFS

Cf. A047999, A101979.

Sequence in context: A127266 A083923 A352824 * A141474 A073424 A135993

Adjacent sequences: A101306 A101307 A101308 * A101310 A101311 A101312

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Dec 23 2004

STATUS

approved