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 A137166 Sequence equals its 4th differences shifted by one index. 1
 1, 3, 7, 15, 32, 70, 156, 349, 778, 1728, 3833, 8505, 18884, 41943, 93160, 206897, 459459, 1020311, 2265815, 5031792, 11174374, 24815508, 55108933, 122382762, 271780616, 603555049, 1340341377, 2976555532, 6610168495, 14679492624 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform yields A079398 without the initial (0,1,1,1). - R. J. Mathar, Apr 09 2008 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-6,5,-1). FORMULA a(n) = 4*a(n-1)-6*a(n-2)+5*a(n-3)-a(n-4). - R. J. Mathar, Apr 09 2008 G.f.: (x^2 - x + 1) / (x^4 - 5*x^3 + 6*x^2 - 4*x + 1). - Alexander R. Povolotsky, Apr 08 2008 MATHEMATICA s = ""; a = 0; b = 1; c = 1; d = 1; For[i = 0, i < 23, a = a + b; s = s <> ToString[a] <> ", "; b = b + c; c = c + d; d = d + a; i++ ]; Print[s] LinearRecurrence[{4, -6, 5, -1}, {1, 3, 7, 15}, 40] (* Vincenzo Librandi, Jun 15 2013 *) PROG (Magma) [n le 4 select 2^n-1 else 4*Self(n-1)-6*Self(n-2)+5*Self(n-3)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jun 15 2013 (PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 5, -6, 4]^n*[1; 3; 7; 15])[1, 1] \\ Charles R Greathouse IV, Oct 03 2016 CROSSREFS Cf. A079398. Sequence in context: A099444 A374678 A132402 * A101890 A307573 A134195 Adjacent sequences: A137163 A137164 A137165 * A137167 A137168 A137169 KEYWORD nonn,easy AUTHOR Vladimir Joseph Stephan Orlovsky, Apr 03 2008 EXTENSIONS Edited by R. J. Mathar, Apr 09 2008 Edited by Bruno Berselli, Apr 07 2011 STATUS approved

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Last modified September 12 11:37 EDT 2024. Contains 375851 sequences. (Running on oeis4.)