A329779 Numbers that are either odd or are congruent to {+-4, +-6, +-8, +-10} (mod 32).

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, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 47, 49, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 79, 81, 83, 85, 86, 87, 88

Offset

1,2

Links

Table of n, a(n) for n=1..66.

G. E. Andrews, Further Problems on Partitions, Amer. Math. Monthly 94 (1987), no. 5, 437-439.

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,-1,2,-1,0,0,0,0,0,-1,2,-1).

Formula

From Colin Barker, Dec 01 2019: (Start)

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)).

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.

(End)

a(n) ~ 4*n/3. - Charles R Greathouse IV, May 21 2026

Maple

lis1:=[4, 6, 8, 10];
f:=proc(n, M, lis) local i;
if member( n mod M, lis) or member( -n mod M, lis) then 1 else 0; fi; end;
a:=[];
for n from 1 to 200 do
if (n mod 2) = 1 or f(n, 32, lis1) = 1 then a:=[op(a), n]; fi; od:
a;

Mathematica

okQ[n_] := OddQ[n] || AnyTrue[{4, 6, 8, 10, 22, 24, 26, 28}, Mod[n, 32] == #&];
Select[Range[100], okQ] (* Jean-François Alcover, Mar 09 2023 *)

Prog

(PARI) a(n)=(4*n+[-3, -1, 1, 0, -1, -2, -3, -4, -5, -6, -7, -5, -3, -1, 1, 3, 2, 1, 0, -1, -2, -3, -4, -5][n%24+1])/3 \\ Charles R Greathouse IV, May 21 2026

Crossrefs

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

Sequence in context: A338477 A039211 A114035 * A072809 A114904 A039220

Adjacent sequences: A329776 A329777 A329778 * A329780 A329781 A329782

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 29 2019

Status

approved