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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
OFFSET
0,2
COMMENTS
Sequence is identical to its shifted third differences.
LINKS
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.
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
Sequence in context: A289692 A074029 A248729 * A367223 A284275 A054159
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, May 15 2008
STATUS
approved