cp's OEIS Frontend

A137824 Index at which A137823(n) occurs first in A137822 (gaps in numbers m such that 3 | sum( Catalan(k), k=1..2m)).

%I A137824 #17 Sep 26 2024 23:34:20
%S A137824 1,3,2,4,12,8,16,48,32,64,192,128,256,768,512,1024,3072,2048,4096,
%T A137824 12288,8192,16384,49152,32768,65536,196608,131072,262144,786432,
%U A137824 524288,1048576,3145728,2097152,4194304,12582912,8388608,16777216,50331648
%N A137824 Index at which A137823(n) occurs first in A137822 (gaps in numbers m such that 3 | sum( Catalan(k), k=1..2m)).
%C A137824 Other characterization of the sequence: concatenate pattern (1,3,2) multiplying it by 4 after each concatenation step. Or: Start with 1,3,2, then iteratively append the whole sequence obtained so far multiplied by 4^(length of the sequence divided by 3)
%C A137824 See A137822 and A137823 for more comments and formulas.
%H A137824 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,4).
%F A137824 If n==2 (mod 3) then a(n) = 3*2^[2*(n-1)/3]; else a(n) = 2^[2*(n-1)/3].
%F A137824 a(n) = 4*a(n-3) for n>3. G.f.: x*(1+x)*(1+2*x)/(1-4*x^3). - _Colin Barker_, Aug 19 2012
%o A137824 (PARI) A137824(n) = if( n%3==2,3,1)<<(2*(n-1)\3)
%o A137824 (PARI) A137824(n) = for( i=1,#A137822, A137822[i]==A137823[n] & return(i))
%o A137824 (PARI) a=[1,3,2]; for( i=1,5, a=concat( a, 4^(#a/3)*a )); a
%Y A137824 Cf. A107755, A122983, A137821, A137822, A137823.
%K A137824 nonn,easy
%O A137824 1,2
%A A137824 _M. F. Hasler_, May 15 2008