A329780 Numbers that are either odd or are congruent to {+-2, +-8, +-12, +-14} (mod 32).

1, 2, 3, 5, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 23, 24, 25, 27, 29, 30, 31, 33, 34, 35, 37, 39, 40, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 59, 61, 62, 63, 65, 66, 67, 69, 71, 72, 73, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 87

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 (1,0,1,-1,0,-1,1,0,1,-1,0,-1,1,0,1,-1,0,-1,1,0,1,-1).

Formula

From Colin Barker, Dec 01 2019: (Start)

G.f.: x*(1 + x)*(1 + x^2 + x^4 - x^5 + x^6 + x^8 + x^12 + x^14 - x^15 + x^16 + x^18 + x^20) / ((1 - x)^2*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)*(1 + x^4)*(1 - x^4 + x^8)).

a(n) = a(n-1) + a(n-3) - a(n-4) - a(n-6) + a(n-7) + a(n-9) - a(n-10) - a(n-12) + a(n-13) + a(n-15) - a(n-16) - a(n-18) + a(n-19) + a(n-21) - a(n-22) for n>22.

(End)

Mathematica

okQ[n_] := OddQ[n] || AnyTrue[{2, 8, 12, 14, 18, 20, 24, 30}, Mod[n, 32] == #&];
Select[Range[100], okQ] (* Jean-François Alcover, Mar 09 2023 *)

Crossrefs

Cf. A329779, A329781, A329782, A329783, A329784.

Sequence in context: A105764 A226811 A227802 * A228856 A274688 A053661

Adjacent sequences: A329777 A329778 A329779 * A329781 A329782 A329783

Keyword

nonn

Author

N. J. A. Sloane, Nov 29 2019

Status

approved