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%I #13 Sep 12 2017 13:18:36
%S 1,2,4,8,15,27,48,86,156,285,521,950,1728,3140,5707,10379,18884,34362,
%T 62520,113737,206897,376362,684652,1245504,2265815,4121947,7498552,
%U 13641134,24815508,45143621,82124025,149397854,271780616,494415932,899427827,1636214155
%N a(n) = 3*a(n-1)-3*a(n-2)+a(n-3)+a(n-4).
%C Sequence is identical to its shifted third differences.
%H Colin Barker, <a href="/A138653/b138653.txt">Table of n, a(n) for n = 0..1000</a>
%H Denis Neiter and Amsha Proag, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Proag/proag3.html">Links Between Sums Over Paths in Bernoulli's Triangles and the Fibonacci Numbers</a>, Journal of Integer Sequences, Vol. 19 (2016), Article 16.8.3.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,1).
%F G.f.: (1-x+x^2+x^3) / (1-3*x+3*x^2-x^3-x^4). - _Colin Barker_, Oct 18 2016
%t LinearRecurrence[{3, -3, 1, 1},{1, 2, 4, 8},14] (* _Ray Chandler_, Sep 23 2015 *)
%o (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
%Y Cf. A098057, A003522.
%K nonn,easy
%O 0,2
%A _Paul Curtz_, May 15 2008
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