|
%I #18 Sep 25 2020 06:31:54
%S 0,0,0,1,2,6,8,16,20,32,36,58,58,86,92,125,122,178,164,228,224,286,
%T 268,382,330,436,424,534,474,660,556,740,692,840,752,1043,846,1094,
%U 1032,1276,1078,1476,1204,1582,1458,1710,1480,2070,1628,2096,1924,2332,1946,2652,2148,2770,2480,2908,2480,3512
%N Number of solutions to the Diophantine equation x1*x2 + x2*x3 + x3*x4 + x4*x5 = n, with all xi >= 1.
%C Related to "Liouville's Last Theorem".
%H George E. Andrews, <a href="http://dx.doi.org/10.1007/BF01608779">Stacked lattice boxes</a>, Ann. Comb. 3 (1999), 115-130. See L_4(n).
%H E. T. Bell, <a href="https://doi.org/10.1090/S0002-9904-1936-06305-6">The form wx+xy+yz+zu</a>, Bull. Amer. Math. Soc., 42 (1936), 377-380.
%e G.f. = x^4 + 2 x^5 + 6 x^6 + 8 x^7 + 16 x^8 + 20 x^9 + 32 x^10 + ...
%p with(numtheory);
%p D00:=n->add(tau(j)*tau(n-j),j=1..n-1);
%p L4:=n->sigma[2](n)-n*sigma[0](n)-D00(n);
%p [seq(L4(n),n=1..60)];
%t a[ n_] := Length @ FindInstance[{x1 > 0, x2 > 0, x3 > 0, x4 > 0, x5 > 0, n == x1 x2 + x2 x3 + x3 x4 + x4 x5}, {x1, x2, x3, x4, x5}, Integers, 10^9]; (* _Michael Somos_, Nov 12 2016 *)
%Y Cf. A189835.
%K nonn
%O 1,5
%A _N. J. A. Sloane_, Jun 17 2011
|
