A114119 Row sums of triangle A114118.
1, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 74, 75, 77, 78, 80, 81, 83, 84, 86, 87, 89, 90, 92, 93, 95, 96, 98, 99, 101, 102, 104, 105
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
Programs
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Mathematica
Join[{1,3},LinearRecurrence[{1,1,-1},{5,6,8},100]] (* Vladimir Joseph Stephan Orlovsky, Jan 31 2012 *)
Formula
a(n) = 3*floor((n + 1)/2) + 2*((n+1) mod 2) - 0^n.
a(n) = Sum_{k=0..n} Sum_{j=0..n} binomial(floor((n + k + j)/3), k)*binomial(k, floor((n + k + j)/3)).
G.f.: 1 - x*(-3 - 2*x + 2*x^2)/((1 + x)*(x - 1)^2). - R. J. Mathar, Oct 25 2011
E.g.f.: ((4 + 3*x)*cosh(x) + 3*(1 + x)*sinh(x) - 2)/2. - Stefano Spezia, Feb 20 2023
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