A138653 a(n) = 3*a(n-1)-3*a(n-2)+a(n-3)+a(n-4).
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
Offset: 0
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).
Programs
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Mathematica
LinearRecurrence[{3, -3, 1, 1},{1, 2, 4, 8},14] (* Ray Chandler, Sep 23 2015 *) -
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
Formula
G.f.: (1-x+x^2+x^3) / (1-3*x+3*x^2-x^3-x^4). - Colin Barker, Oct 18 2016
Comments