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A085405 Common residues of binomial(3n+2,n+1)/(3n+2) modulo 2. 5
1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The positions of ones are given by A022340 and runs of zeros are given by A085407: both are related to the Fibonacci sequence.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65539

Index entries for characteristic functions

FORMULA

a(n) = C(3n+2, n+1)/(3n+2) (Mod 2) = A006013(n) (Mod 2), where A006013 is the self-convolution of A001764 (ternary trees).

a(n) = A323239(A005940(1+n)). - Antti Karttunen, Jan 12 2019

PROG

(PARI) A085405(n) = ((binomial((3*n)+2, n+1)/((3*n)+2))%2); \\ Antti Karttunen, Jan 12 2019

(PARI) A085405(n) = if(n%2, 0, while(n>0, my(nextn=(n>>1)); if(1==(nextn%2)*(n%2), return(0)); n = nextn); (1)); \\ (Much faster than above program) - Antti Karttunen, Jan 12 2019

CROSSREFS

Cf. A005940, A006013, A022340 (ones), A085407 (zeros), A085357, A277332, A323239.

Sequence in context: A171894 A284957 A316533 * A036988 A108357 A309848

Adjacent sequences:  A085402 A085403 A085404 * A085406 A085407 A085408

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 29 2003

STATUS

approved

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Last modified January 29 03:07 EST 2022. Contains 350672 sequences. (Running on oeis4.)