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A210377
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Number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = n + 5.
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2
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0, 0, 4, 31, 80, 146, 224, 315, 420, 540, 676, 829, 1000, 1190, 1400, 1631, 1884, 2160, 2460, 2785, 3136, 3514, 3920, 4355, 4820, 5316, 5844, 6405, 7000, 7630, 8296, 8999, 9740, 10520, 11340, 12201, 13104, 14050, 15040, 16075, 17156, 18284
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OFFSET
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0,3
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COMMENTS
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A210376 is also the number of 2 X 2 matrices with all terms in {0,1,...,n} and (sum of terms) = 3n - 5.
See A210000 for a guide to related sequences.
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LINKS
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FORMULA
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G.f.: x^2*(4 + 15*x - 20*x^2 - 4*x^3 + 6*x^5) / (1 - x)^4.
a(n) = (-504 + 146*n + 21*n^2 + n^3) / 6 for n>3.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.
(End)
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MATHEMATICA
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a = 0; b = n; z1 = 45;
t[n_] := t[n] = Flatten[Table[w + x + y + z, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
Table[c[n, n + 5], {n, 0, z1}] (* A210377 *)
Table[c[n, 3 n - 5], {n, 0, z1}] (* A210377 *)
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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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