A114119 - OEIS

%I #22 Feb 21 2023 10:37:11

%S 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,

%T 39,41,42,44,45,47,48,50,51,53,54,56,57,59,60,62,63,65,66,68,69,71,72,

%U 74,75,77,78,80,81,83,84,86,87,89,90,92,93,95,96,98,99,101,102,104,105

%N Row sums of triangle A114118.

%C Taken modulo 3 yields 1,0,2,0,2,0,2,0,2,...; a(n) is congruent to 0 or 2 (mod 3) for n > 0.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F a(n) = 3*floor((n + 1)/2) + 2*((n+1) mod 2) - 0^n.

%F a(n) = Sum_{k=0..n} Sum_{j=0..n} binomial(floor((n + k + j)/3), k)*binomial(k, floor((n + k + j)/3)).

%F G.f.: 1 - x*(-3 - 2*x + 2*x^2)/((1 + x)*(x - 1)^2). - _R. J. Mathar_, Oct 25 2011

%F E.g.f.: ((4 + 3*x)*cosh(x) + 3*(1 + x)*sinh(x) - 2)/2. - _Stefano Spezia_, Feb 20 2023

%t Join[{1,3},LinearRecurrence[{1,1,-1},{5,6,8},100]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 31 2012 *)

%Y Cf. A007494, A049636, A045506.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Nov 13 2005