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%I #13 Oct 23 2022 01:21:37
%S 1,3,5,11,17,25,35,45,59,73,89,107,125,147,169,193,219,245,275,305,
%T 337,371,405,443,481,521,563,605,651,697,745,795,845,899,953,1009,
%U 1067,1125,1187,1249,1313,1379,1445,1515,1585,1657,1731,1805,1883
%N Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w+4x+5y=0.
%C For a guide to related sequences, see A211422.
%F Conjectures from _Colin Barker_, May 15 2017: (Start)
%F G.f.: (1 + x + 4*x^3 + x^5 + x^6) / ((1 - x)^3*(1 + x + x^2 + x^3 + x^4)).
%F a(n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7) for n > 6. (End)
%F Conjecture: a(n) ~ 4*n^2/5. - _Stefano Spezia_, Oct 17 2022
%t t[n_] := t[n] = Flatten[Table[w + 4 x + 5 y, {w, -n, n}, {x, -n, n}, {y, -n, n}]]
%t c[n_] := Count[t[n], 0]
%t t = Table[c[n], {n, 0, 70}] (* A211435 *)
%t (t - 1)/2 (* integers *)
%Y Cf. A211422.
%K nonn
%O 0,2
%A _Clark Kimberling_, Apr 11 2012
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