A111019 - OEIS

A111019

Indices of Catalan numbers that are == 1 mod 3 (cf. A000108).

1, 11, 12, 13, 29, 30, 31, 35, 36, 37, 83, 84, 85, 89, 90, 91, 107, 108, 109, 119, 120, 121, 245, 246, 247, 251, 252, 253, 269, 270, 271, 281, 282, 283, 323, 324, 325, 335, 336, 337, 353, 354, 355, 359, 360, 361, 731, 732, 733, 737, 738, 739, 755

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OFFSET

1,2

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(3k) = a(3k-1)+1 and a(3k+1) = a(3k-1)+2 for k >= 1. - Robert Israel, Jun 30 2020

MAPLE

filter:= proc(n) local L1, L2, L3;

L1:= convert(2*n, base, 3);

L2:= convert(n, base, 3);

L3:= convert(n-1, base, 3);

mul(binomial(L1[i], L2[i]), i=1..nops(L2)) - mul(binomial(L1[i], L3[i]), i=1..nops(L3)) mod 3 = 1

end proc:

select(filter, [$1..1000]); # Robert Israel, Jun 30 2020

MATHEMATICA

Flatten[Position[CatalanNumber[Range[1000]], _?(Mod[#, 3]==1&)]] (* Harvey P. Dale, Jun 19 2014 *)

CROSSREFS

Cf. A000108, A111020.

Sequence in context: A185300 A097932 A031300 * A306583 A048035 A048015

Adjacent sequences: A111016 A111017 A111018 * A111020 A111021 A111022

KEYWORD

nonn,look

AUTHOR

Robert G. Wilson v, Sep 09 2005

STATUS

approved