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A211481 Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w+2x+3y=n. 2

%I

%S 1,3,8,16,26,38,54,71,91,114,139,166,197,229,264,302,342,384,430,477,

%T 527,580,635,692,753,815,880,948,1018,1090,1166,1243,1323,1406,1491,

%U 1578,1669,1761,1856,1954,2054,2156,2262,2369,2479,2592,2707

%N Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w+2x+3y=n.

%C For a guide to related sequences, see A211422.

%F Conjecture: a(n) = a(n-1)+a(n-2)-a(n-4)-a(n-5)+a(n-6) for n>5. - _Colin Barker_, Nov 08 2014

%F Empirical g.f.: -(3*x^4+5*x^3+4*x^2+2*x+1) / ((x-1)^3*(x+1)*(x^2+x+1)). - _Colin Barker_, Nov 08 2014

%t t[n_] := t[n] = Flatten[Table[w + 2 x + 3 y - n, {w, -n, n}, {x, -n, n}, {y, -n, n}]]

%t c[n_] := Count[t[n], 0]

%t t = Table[c[n], {n, 0, 70}] (* A211481 *)

%Y Cf. A211422.

%K nonn

%O 0,2

%A _Clark Kimberling_, Apr 12 2012

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Last modified September 20 14:44 EDT 2021. Contains 347586 sequences. (Running on oeis4.)