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 A084567 Binomial transform of (1,-1,4,-16,64,-256,1024,...) = (3*0^n-(-4)^n)/4. 6
 1, 0, 3, -6, 21, -60, 183, -546, 1641, -4920, 14763, -44286, 132861, -398580, 1195743, -3587226, 10761681, -32285040, 96855123, -290565366, 871696101, -2615088300, 7845264903, -23535794706, 70607384121, -211822152360, 635466457083, -1906399371246 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Partial sums of (1,-1,3,-9,27,-81,....) (with g.f. (1+2x)/(1+3x) ). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (-2,3) FORMULA G.f.: (1+2*x)/((1-x)*(1+3*x)). G.f.: 1+ x -x/Q(0), where Q(k) = 1 + 3*x^2 + (3*k+4)*x - x*(3*k+1 + 3*x)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 07 2013 MATHEMATICA CoefficientList[Series[(1 + 2 x)/((1 - x) (1 + 3 x)), {x, 0, 50}], x] (* Vincenzo Librandi, Oct 07 2013 *) LinearRecurrence[{-2, 3}, {1, 0}, 30] (* Harvey P. Dale, Aug 26 2024 *) PROG (PARI) Vec((1+2*x)/((1-x)*(1+3*x))+O(x^66)) \\ Joerg Arndt, Jul 14 2013 (Magma) I:=[1, 0]; [n le 2 select I[n] else -2*Self(n-1)+3*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 07 2013 CROSSREFS Cf. A054878 (absolute values). Sequence in context: A148623 A259273 A054878 * A294527 A261582 A135686 Adjacent sequences: A084564 A084565 A084566 * A084568 A084569 A084570 KEYWORD easy,sign AUTHOR Paul Barry, May 30 2003 EXTENSIONS Removed incorrect g.f. and e.g.f., Joerg Arndt, Jul 14 2013 STATUS approved

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Last modified September 9 22:43 EDT 2024. Contains 375765 sequences. (Running on oeis4.)