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A242658
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a(n) = 3*n^2 - 3*n + 2.
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4
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2, 2, 8, 20, 38, 62, 92, 128, 170, 218, 272, 332, 398, 470, 548, 632, 722, 818, 920, 1028, 1142, 1262, 1388, 1520, 1658, 1802, 1952, 2108, 2270, 2438, 2612, 2792, 2978, 3170, 3368, 3572, 3782, 3998, 4220, 4448, 4682, 4922, 5168, 5420, 5678, 5942, 6212, 6488, 6770, 7058, 7352
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OFFSET
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0,1
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COMMENTS
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An exercise in Smith (1950), my secondary school algebra book.
For n > 0, also the number of (not necessarily maximal) cliques in the (n-1)-triangular grid graph. - Eric W. Weisstein, Nov 29 2017
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REFERENCES
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C. Smith, A Treatise on Algebra, Macmillan, London, 5th ed., 1950, p. 429, Example 2(i).
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LINKS
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Eric Weisstein's World of Mathematics, Clique
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FORMULA
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a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
G.f.: 2*(-4*x^2 + 2*x - 1)/(x - 1)^3. (End)
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {2, 8, 20}, {0, 20}] (* Eric W. Weisstein, Nov 29 2017 *)
CoefficientList[Series[-2 (1 - 2 x + 4 x^2)/(-1 + x)^3, {x, 0, 20}], x] (* Eric W. Weisstein, Nov 29 2017 *)
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PROG
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CROSSREFS
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A077588 is the same except for the initial term.
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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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