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%I #14 Nov 18 2021 13:24:02
%S 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,
%T 61,49,70,56,80,64,91,72,102,81,114,90,127,100,140,110,154,121,169,
%U 132,184,144,200,156,217,169,234,182,252,196,271,210,290,225,310,240,331,256,352
%N Number of partitions of n into 3 parts with at least 1 odd part.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,1,0,0,0,-1,0,-1,0,1).
%F 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)).
%F 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
%F a(n) = a(n-2)+a(n-4)-a(n-8)-a(n-10)+a(n-12). - _Wesley Ivan Hurt_, Nov 18 2021
%t 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 *)
%Y Cf. A069905.
%K nonn,easy
%O 1,5
%A _Wesley Ivan Hurt_, Oct 21 2021