A329782 Numbers that are congruent to {+-1, +-4, +-5, +-6, +-7, +-9, +-10, +-11, +-13, +-15, +-16, +-19} (mod 40).

1, 4, 5, 6, 7, 9, 10, 11, 13, 15, 16, 19, 21, 24, 25, 27, 29, 30, 31, 33, 34, 35, 36, 39, 41, 44, 45, 46, 47, 49, 50, 51, 53, 55, 56, 59, 61, 64, 65, 67, 69, 70, 71, 73, 74, 75, 76, 79, 81, 84, 85, 86, 87, 89, 90, 91, 93, 95, 96, 99, 101, 104, 105, 107, 109

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

Formula

From Colin Barker, Dec 01 2019: (Start)

G.f.: x*(1 + 3*x + x^2 + x^3 + x^4 + 2*x^5 + x^6 + x^7 + 2*x^8 + 2*x^9 + x^10 + 3*x^11 + 2*x^12 + 3*x^13 + x^14 + 2*x^15 + 2*x^16 + x^17 + x^18 + 2*x^19 + x^20 + x^21 + x^22 + 3*x^23 + x^24) / ((1 - x)^2*(1 + x)*(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) = a(n-1) + a(n-24) - a(n-25) for n>25.

(End)

Mathematica

okQ[n_] := AnyTrue[Join[lis = {1, 4, 5, 6, 7, 9, 10, 11, 13, 15, 16, 19}, 40 - lis], Mod[n, 40] == # &];
Select[Range[200], okQ] (* Jean-François Alcover, Mar 09 2023 *)

Crossrefs

Cf. A329779, A329780, A329781, A329783, A329784.

Sequence in context: A347932 A242337 A201739 * A218044 A066485 A079445

Adjacent sequences: A329779 A329780 A329781 * A329783 A329784 A329785

Keyword

nonn

Author

N. J. A. Sloane, Nov 29 2019

Status

approved