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A061982
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a(n) = 3^n - (n+1)*(n+2)/2.
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2
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0, 0, 3, 17, 66, 222, 701, 2151, 6516, 19628, 58983, 177069, 531350, 1594218, 4782849, 14348771, 43046568, 129139992, 387420299, 1162261257, 3486784170, 10460352950, 31381059333, 94143178527, 282429536156, 847288609092
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = 3^n - binomial(n+2, 2).
G.f.: x^2*(3-x)/((1-x)^3 * (1-3*x)).
E.g.f.: exp(3*x) - (1/2)*(2 + 4*x + x^2)*exp(x). (End)
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MATHEMATICA
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LinearRecurrence[{6, -12, 10, -3}, {0, 0, 3, 17}, 40] (* G. C. Greubel, Jun 13 2022 *)
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PROG
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(PARI) { for (n=0, 200, write("b061982.txt", n, " ", 3^n - (n + 1)*(n + 2)/2) ) } \\ Harry J. Smith, Jul 29 2009
(Magma) [3^n -Binomial(n+2, 2): n in [0..40]]; // G. C. Greubel, Jun 13 2022
(SageMath) [3^n -binomial(n+2, 2) for n in (0..40)] # G. C. Greubel, Jun 13 2022
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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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