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%I #10 Jan 21 2022 07:52:29
%S 0,0,3,5,7,9,11,13,24,28,32,36,40,44,48,52,73,79,85,91,97,103,109,115,
%T 121,127,160,168,176,184,192,200,208,216,224,232,240,248,295,305,315,
%U 325,335,345,355,365,375,385,395,405,415,425,488,500,512,524,536,548,560,572,584
%N a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = floor((n+1)/2), s = A023531, t = (odd natural numbers).
%H G. C. Greubel, <a href="/A024323/b024323.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*(2*n -2*j + 1). - _G. C. Greubel_, Jan 20 2022
%t A023531[n_]:= SquaresR[1, 8n+9]/2;
%t a[n_]:= Sum[A023531[j]*(2*n-2*j+1), {j, Floor[(n+1)/2]}];
%t Table[a[n], {n, 70}] (* _G. C. Greubel_, Jan 20 2022 *)
%o (Magma)
%o A023531:= func< n | IsIntegral( (Sqrt(8*n+9) - 3)/2 ) select 1 else 0 >;
%o [ (&+[A023531(j)*(2*n-2*j+1): j in [1..Floor((n+1)/2)]]) : n in [1..70]]; // _G. C. Greubel_, Jan 20 2022
%o (Sage)
%o def A023531(n):
%o if ((sqrt(8*n+9) -3)/2).is_integer(): return 1
%o else: return 0
%o [sum( A023531(j)*(2*n-2*j+1) for j in (1..floor((n+1)/2)) ) for n in (1..70)] # _G. C. Greubel_, Jan 20 2022
%Y Cf. A024312, A024313, A024314, A024315, A024316, A024317, A024318, A024319, A024320, A024321, A024322, A024324, A024325, A024326, A024327.
%Y Cf. A023531.
%K nonn
%O 1,3
%A _Clark Kimberling_
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