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

0,2

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