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a(n) = s(1)*s(n) + s(2)*s(n-1) + ... + s(k)*s(n+1-k), where k = floor((n+1)/2), s = A023531.
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%I #15 Jan 09 2024 16:07:16

%S 0,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,2,0,0,1,0,1,0,

%T 1,1,0,0,2,1,0,0,1,0,1,1,0,2,0,0,0,1,1,1,1,0,1,1,0,0,1,1,1,0,0,1,1,0,

%U 2,1,0,0,2,0,0,0,0,3,0,1,1,0,0,1,1,0,1,1,0,1

%N a(n) = s(1)*s(n) + s(2)*s(n-1) + ... + s(k)*s(n+1-k), where k = floor((n+1)/2), s = A023531.

%H Reinhard Zumkeller, <a href="/A024316/b024316.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*A023531(n-j+1). - _G. C. Greubel_, Jan 17 2022

%t A023531[n_]:= SquaresR[1, 8n+9]/2;

%t a[n_]:= a[n]= Sum[A023531[j]*A023531[n-j+1], {j, Floor[(n+1)/2]}];

%t Table[a[n], {n, 110}] (* _G. C. Greubel_, Jan 17 2022 *)

%o (Haskell)

%o a024316 n = sum $ take (div (n + 1) 2) $ zipWith (*) zs $ reverse zs

%o where zs = take n $ tail a023531_list

%o -- _Reinhard Zumkeller_, Feb 14 2015

%o (Magma)

%o A023531:= func< n | IsIntegral( (Sqrt(8*n+9) - 3)/2 ) select 1 else 0 >;

%o [ (&+[A023531(j)*A023531(n-j+1): j in [1..Floor((n+1)/2)]]) : n in [1..110]]; // _G. C. Greubel_, Jan 17 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)*A023531(n-j+1) for j in (1..floor((n+1)/2)) ) for n in (1..110)] # _G. C. Greubel_, Jan 17 2022

%Y Cf. A024312, A024313, A024314, A024315, A024317, A024318, A024319, A024320, A024321, A024322, A024323, A024324, A024325, A024326, A024327.

%Y Cf. A023531.

%K nonn

%O 1,28

%A _Clark Kimberling_