A062547 - OEIS

%I #30 Mar 16 2024 11:30:55

%S 1,3,5,7,17,19,53,55,161,163,485,487,1457,1459,4373,4375,13121,13123,

%T 39365,39367,118097,118099,354293,354295,1062881,1062883,3188645,

%U 3188647,9565937,9565939,28697813,28697815,86093441,86093443,258280325,258280327,774840977

%N a(n) is least odd integer not a partial sum of 1, 3, ..., a(n-1).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,3,3).

%F a(2*n) = A048473(n); a(2n+1) = a(2n)+2.

%F For n > 0, a(2*n) = 3*a(2*n-1) - 4; a(2*n+1) = a(2*n) + 2 = A052919(n+1).

%F From _Bruno Berselli_, Jan 28 2011: (Start)

%F G.f.: (1+4*x+5*x^2)/((1+x)*(1-3*x^2)).

%F a(n) = -a(n-1) + 3*a(n-2) + 3*a(n-3) for n > 2.

%F a(n) = 2*3^((2*n + (-1)^n - 1)/4) - (-1)^n. (End)

%e Partial sums of 1;3;5 are 1;3;4;5;6;8;9 and 7 is the least missing odd integer, hence the next term is 7.

%t Table[ -1+ 2 3^Floor[k/2]+2 Mod[k, 2], {k, 0, 36}]

%t LinearRecurrence[{-1,3,3},{1,3,5},40] (* _Harvey P. Dale_, Jul 14 2018 *)

%Y Cf. A048473, A052919, A062548.

%K nonn,easy

%O 0,2

%A _Wouter Meeussen_, Jun 26 2001

%E Edited by _Michel Marcus_, Mar 16 2024