A348543 Number of partitions of n into 3 parts with at least 1 odd part.

0, 0, 1, 1, 2, 2, 4, 4, 7, 6, 10, 9, 14, 12, 19, 16, 24, 20, 30, 25, 37, 30, 44, 36, 52, 42, 61, 49, 70, 56, 80, 64, 91, 72, 102, 81, 114, 90, 127, 100, 140, 110, 154, 121, 169, 132, 184, 144, 200, 156, 217, 169, 234, 182, 252, 196, 271, 210, 290, 225, 310, 240, 331, 256, 352

Offset

1,5

Links

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

Index entries for sequences related to partitions

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

Formula

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (1-((j+1) mod 2)*((i+1) mod 2)*((n-i-j+1) mod 2)).

G.f.: -x^3*(x^6+x^5+x^4+x^3+x^2+x+1)/(x^12-x^10-x^8+x^4+x^2-1). - Alois P. Heinz, Oct 22 2021

a(n) = a(n-2)+a(n-4)-a(n-8)-a(n-10)+a(n-12). - Wesley Ivan Hurt, Nov 18 2021

Mathematica

a[n_] := Sum[1 - Mod[j + 1, 2] * Mod[i + 1, 2] * Mod[n - i - j + 1, 2], {j, 1, Floor[n/3]}, {i, j, Floor[(n - j)/2]}]; Array[a, 100] (* Amiram Eldar, Oct 22 2021 *)

Crossrefs

Cf. A069905.

Sequence in context: A341949 A338333 A287144 * A085893 A341950 A230167

Adjacent sequences: A348540 A348541 A348542 * A348544 A348545 A348546

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 21 2021

Status

approved