A329779 - OEIS

%I #27 Mar 20 2023 06:21:29

%S 1,3,4,5,6,7,8,9,10,11,13,15,17,19,21,22,23,24,25,26,27,28,29,31,33,

%T 35,36,37,38,39,40,41,42,43,45,47,49,51,53,54,55,56,57,58,59,60,61,63,

%U 65,67,68,69,70,71,72,73,74,75,77,79,81,83,85,86,87,88

%N Numbers that are either odd or are congruent to {+-4, +-6, +-8, +-10} (mod 32).

%H G. E. Andrews, <a href="http://www.jstor.org/stable/2322727">Further Problems on Partitions</a>, Amer. Math. Monthly 94 (1987), no. 5, 437-439.

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,-1,2,-1,0,0,0,0,0,-1,2,-1).

%F From _Colin Barker_, Dec 01 2019: (Start)

%F G.f.: x*(1 + x)*(1 - x^2 + x^3 - x^4 + x^5 - x^6 + x^7 + x^9 - x^10 + x^11 - x^12 + x^13 - x^14 + x^16) / ((1 - x)^2*(1 - x + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)*(1 - x^4 + x^8)).

%F a(n) = 2*a(n-1) - a(n-2) - a(n-8) + 2*a(n-9) - a(n-10) - a(n-16) + 2*a(n-17) - a(n-18) for n>18.

%F (End)

%p lis1:=[4,6,8,10];

%p f:=proc(n,M,lis) local i;

%p if member( n mod M, lis) or member( -n mod M, lis) then 1 else 0; fi; end;

%p a:=[];

%p for n from 1 to 200 do

%p if (n mod 2) = 1 or f(n,32,lis1) = 1 then a:=[op(a), n]; fi; od:

%p a;

%t okQ[n_] := OddQ[n] || AnyTrue[{4, 6, 8, 10, 22, 24, 26, 28}, Mod[n, 32] == #&];

%t Select[Range[100], okQ] (* _Jean-François Alcover_, Mar 09 2023 *)

%Y Cf. A329780, A329781, A329782, A329783, A329784.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Nov 29 2019