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A211543
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Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w=3x+5y.
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2
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0, 0, 0, 0, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 14, 16, 18, 21, 23, 25, 28, 31, 34, 37, 40, 43, 47, 51, 54, 58, 62, 66, 71, 75, 79, 84, 89, 94, 99, 104, 109, 115, 121, 126, 132, 138, 144, 151, 157, 163, 170, 177, 184, 191, 198, 205, 213, 221, 228, 236, 244
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OFFSET
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0,8
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COMMENTS
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For a guide to related sequences, see A211422.
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LINKS
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FORMULA
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a(n) = a(n-1) + a(n-3) - a(n-4) + a(n-5) - a(n-6) - a(n-8) + a(n-9).
G.f.: x^4*(1 + x^4) / ((1 - x)^3*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Dec 03 2017
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MATHEMATICA
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t[n_] := t[n] = Flatten[Table[-2 w + 3 x + 5 y, {w, 1, n}, {x, 1, n}, {y, 1, n}]]
c[n_] := Count[t[n], 0]
t = Table[c[n], {n, 0, 70}] (* A211543 *)
FindLinearRecurrence[t]
LinearRecurrence[{1, 0, 1, -1, 1, -1, 0, -1, 1}, {0, 0, 0, 0, 1, 1, 1, 2, 3}, 63] (* Ray Chandler, Aug 02 2015 *)
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PROG
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(PARI) concat(vector(4), Vec(x^4*(1 + x^4) / ((1 - x)^3*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)) + O(x^40))) \\ Colin Barker, Dec 03 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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