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%I #10 Jan 24 2022 07:04:06
%S 0,0,3,4,7,11,18,29,58,94,152,246,398,644,1042,1686,2804,4537,7341,
%T 11878,19219,31097,50316,81413,131729,213142,345714,559377,905091,
%U 1464468,2369559,3834027,6203586
%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 = (Lucas numbers).
%H G. C. Greubel, <a href="/A024319/b024319.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Sum_{j=1..floor((n+1)/2)} A023531(j)*Lucas(n-j+1). - _G. C. Greubel_, Jan 19 2022
%t A023531[n_]:= SquaresR[1, 8n+9]/2;
%t a[n_]:= Sum[A023531[j]*LucasL[n-j+1], {j, Floor[(n+1)/2]}];
%t Table[a[n], {n, 40}] (* _G. C. Greubel_, Jan 19 2022 *)
%o (Magma)
%o A023531:= func< n | IsIntegral( (Sqrt(8*n+9) -3)/2 ) select 1 else 0 >;
%o [ (&+[A023531(j)*Lucas(n-j+1): j in [1..Floor((n+1)/2)]]) : n in [1..40]]; // _G. C. Greubel_, Jan 19 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)*lucas_number2(n-j+1,1,-1) for j in (1..floor((n+1)/2)) ) for n in (1..40)] # _G. C. Greubel_, Jan 19 2022
%Y Cf. A024312, A024313, A024314, A024315, A024316, A024317, A024318, A024320, A024321, A024322, A024323, A024324, A024325, A024326, A024327.
%Y Cf. A000032, A023531.
%K nonn
%O 1,3
%A _Clark Kimberling_
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