cp's OEIS Frontend

A024317 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 = A023532.

%I A024317 #14 May 15 2025 15:58:25
%S A024317 0,0,0,1,1,0,1,1,1,1,2,2,1,2,1,2,2,2,3,3,2,2,3,2,3,3,3,2,4,4,3,4,3,4,
%T A024317 3,3,4,4,3,4,5,5,4,5,4,4,5,3,5,5,5,4,5,5,5,6,5,5,6,6,5,5,5,6,6,5,5,6,
%U A024317 5,6,7,7,5,7,7,7,7,4,7,6,6,7,7,6,6,7,7,7,8,7,6,8,8,7,8,7,7,7,7,8,8,8,6,8,7,8,8,7,8,9,8,8
%N A024317 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 = A023532.
%H A024317 G. C. Greubel, <a href="/A024317/b024317.txt">Table of n, a(n) for n = 1..1000</a>
%F A024317 a(n) = Sum_{k=1..floor((n+1)/2)} A023531(k)*A023532(n-k+1). - _G. C. Greubel_, Jan 19 2022
%t A024317 A023531[n_]:= SquaresR[1, 8n+9]/2;
%t A024317 a[n_]:= Sum[A023531[j]*(1 - A023531[n-j+1]), {j, Floor[(n+1)/2]}];
%t A024317 Table[a[n], {n, 90}] (* _G. C. Greubel_, Jan 19 2022 *)
%o A024317 (Magma)
%o A024317 A023531:= func< n | IsIntegral( (Sqrt(8*n+9) -3)/2 ) select 1 else 0 >;
%o A024317 [ (&+[A023531(j)*(1 - A023531(n-j+1)): j in [1..Floor((n+1)/2)]]) : n in [1..90]]; // _G. C. Greubel_, Jan 19 2022
%o A024317 (Sage)
%o A024317 def A023531(n):
%o A024317     if ((sqrt(8*n+9) -3)/2).is_integer(): return 1
%o A024317     else: return 0
%o A024317 [sum( A023531(j)*(1-A023531(n-j+1)) for j in (1..floor((n+1)/2)) ) for n in (1..90)] # _G. C. Greubel_, Jan 19 2022
%Y A024317 Cf. A024312, A024313, A024314, A024315, A024316, A024318, A024319, A024320, A024321, A024322, A024323, A024324, A024325, A024326, A024327.
%Y A024317 Cf. A023531. A023532.
%K A024317 nonn
%O A024317 1,11
%A A024317 _Clark Kimberling_