A329781 Numbers that are congruent to {+-1, +-3, +-4, +-5, +-9, +-10, +-11, +-14, +-15, +-16, +-17, +-19} (mod 40).

1, 3, 4, 5, 9, 10, 11, 14, 15, 16, 17, 19, 21, 23, 24, 25, 26, 29, 30, 31, 35, 36, 37, 39, 41, 43, 44, 45, 49, 50, 51, 54, 55, 56, 57, 59, 61, 63, 64, 65, 66, 69, 70, 71, 75, 76, 77, 79, 81, 83, 84, 85, 89, 90, 91, 94, 95, 96, 97, 99, 101, 103, 104, 105, 106

Offset

1,2

Links

Table of n, a(n) for n=1..65.

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,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-2,2,-1).

Formula

From Colin Barker, Dec 01 2019: (Start)

G.f.: x*(1 + x)*(1 + x^3 + 2*x^4 - 4*x^5 + 7*x^6 - 7*x^7 + 8*x^8 - 8*x^9 + 9*x^10 - 8*x^11 + 9*x^12 - 8*x^13 + 8*x^14 - 7*x^15 + 7*x^16 - 4*x^17 + 2*x^18 + x^19 + x^22) / ((1 - x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)*(1 + x^4)*(1 - x^4 + x^8)).

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - 2*a(n-6) + 2*a(n-7) - 2*a(n-8) + 2*a(n-9) - 2*a(n-10) + 2*a(n-11) - 2*a(n-12) + 2*a(n-13) - 2*a(n-14) + 2*a(n-15) - 2*a(n-16) + 2*a(n-17) - 2*a(n-18) + 2*a(n-19) - 2*a(n-20) + 2*a(n-21) - 2*a(n-22) + 2*a(n-23) - a(n-24) for n>24.

(End)

Maple

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;
lis3:=[1, 3, 4, 5, 9, 10, 11, 14, 15, 16, 17, 19];
lis := lis3;
a:=[];
for n from 1 to 200 do
if f(n, 40, lis) = 1 then a:=[op(a), n]; fi; od:
a;

Mathematica

okQ[n_] := AnyTrue[Join[lis = {1, 3, 4, 5, 9, 10, 11, 14, 15, 16, 17, 19}, 40 - lis], Mod[n, 40] == #&];
Select[Range[200], okQ] (* Jean-François Alcover, Mar 09 2023 *)

Crossrefs

Cf. A329779, A329780, A329782, A329783, A329784.

Sequence in context: A246303 A362461 A285161 * A139531 A047249 A327257

Adjacent sequences: A329778 A329779 A329780 * A329782 A329783 A329784

Keyword

nonn

Author

N. J. A. Sloane, Nov 29 2019

Status

approved