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 A138653 a(n) = 3*a(n-1)-3*a(n-2)+a(n-3)+a(n-4). 1
 1, 2, 4, 8, 15, 27, 48, 86, 156, 285, 521, 950, 1728, 3140, 5707, 10379, 18884, 34362, 62520, 113737, 206897, 376362, 684652, 1245504, 2265815, 4121947, 7498552, 13641134, 24815508, 45143621, 82124025, 149397854, 271780616, 494415932, 899427827, 1636214155 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sequence is identical to its shifted third differences. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Denis Neiter and Amsha Proag, Links Between Sums Over Paths in Bernoulli's Triangles and the Fibonacci Numbers, Journal of Integer Sequences, Vol. 19 (2016), Article 16.8.3. Index entries for linear recurrences with constant coefficients, signature (3,-3,1,1). FORMULA G.f.: (1-x+x^2+x^3) / (1-3*x+3*x^2-x^3-x^4). - Colin Barker, Oct 18 2016 MATHEMATICA LinearRecurrence[{3, -3, 1, 1}, {1, 2, 4, 8}, 14] (* Ray Chandler, Sep 23 2015 *) PROG (PARI) Vec((1-x+x^2+x^3)/(1-3*x+3*x^2-x^3-x^4) + O(x^50)) \\ Colin Barker, Oct 18 2016 CROSSREFS Cf. A098057, A003522. Sequence in context: A289692 A074029 A248729 * A367223 A284275 A054159 Adjacent sequences: A138650 A138651 A138652 * A138654 A138655 A138656 KEYWORD nonn,easy AUTHOR Paul Curtz, May 15 2008 STATUS approved

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Last modified May 27 21:52 EDT 2024. Contains 372882 sequences. (Running on oeis4.)