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 A061982 a(n) = 3^n - (n+1)*(n+2)/2. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Harry J. Smith, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (6,-12,10,-3). FORMULA From G. C. Greubel, Jun 13 2022: (Start) 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) MATHEMATICA LinearRecurrence[{6, -12, 10, -3}, {0, 0, 3, 17}, 40] (* G. C. Greubel, Jun 13 2022 *) PROG (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 CROSSREFS Column of A061980. Cf. A000217, A000244. Sequence in context: A174285 A227427 A120386 * A101562 A034566 A357923 Adjacent sequences: A061979 A061980 A061981 * A061983 A061984 A061985 KEYWORD nonn,easy AUTHOR Henry Bottomley, May 24 2001 STATUS approved

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Last modified June 8 11:34 EDT 2023. Contains 363164 sequences. (Running on oeis4.)