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A183954
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Number of strings of numbers x(i=1..3) in 0..n with sum i^2*x(i) equal to n*9.
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2
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1, 2, 2, 3, 4, 6, 7, 9, 12, 14, 17, 19, 22, 25, 29, 32, 36, 41, 45, 50, 54, 59, 64, 70, 75, 81, 88, 94, 101, 107, 114, 121, 129, 136, 144, 153, 161, 170, 178, 187, 196, 206, 215, 225, 236, 246, 257, 267, 278, 289, 301, 312, 324, 337, 349, 362, 374, 387, 400, 414, 427, 441
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-9) - 2*a(n-10) + a(n-11).
Empirical g.f.: x*(1 + x)*(1 - x + x^3 - x^4 + 2*x^5 - 3*x^6 + 4*x^7 - 3*x^8 + x^9) / ((1 - x)^3*(1 + x + x^2)*(1 + x^3 + x^6)). - Colin Barker, Apr 07 2018
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EXAMPLE
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All solutions for n=3:
..0....1
..0....2
..3....2
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MATHEMATICA
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r[n_, k_, s_] := r[n, k, s] = Which[s < 0, 0, n == 0, If[s == 0, 1, 0], True, Sum[r[n - 1, k, s - c*n^2], {c, 0, k}]];
T[n_, k_] := r[n, k, k*n^2];
a[n_] := T[3, n];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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