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A079284 Diagonal sums of triangle A008949.

%I A079284 #25 Sep 08 2022 08:45:08
%S A079284 1,1,3,4,9,13,26,39,73,112,201,313,546,859,1469,2328,3925,6253,10434,
%T A079284 16687,27633,44320,72977,117297,192322,309619,506037,815656,1329885,
%U A079284 2145541,3491810,5637351,9161929,14799280,24026745,38826025,62983842,101809867,165055853,266865720
%N A079284 Diagonal sums of triangle A008949.
%C A079284 a(2n) - a(2n-1) = Fibonacci(2n+1).
%C A079284 Diagonal sums of triangle A054450. - _Paul Barry_, Oct 23 2004
%H A079284 Vincenzo Librandi, <a href="/A079284/b079284.txt">Table of n, a(n) for n = 0..1000</a>
%H A079284 Donatella Merlini, Massimo Nocentini, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL21/Merlini/merlini5.html">Algebraic Generating Functions for Languages Avoiding Riordan Patterns</a>, Journal of Integer Sequences, Vol. 21 (2018), Article 18.1.3.
%H A079284 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-2,-2).
%F A079284 a(n) = Sum_{j=0..floor(n/2)} Sum_{i=0..j} binomial(n-j, i).
%F A079284 a(n) = Fibonacci(n+3) - 2^floor((n+1)/2). - _Vladeta Jovovic_, Feb 12 2003
%F A079284 G.f.: (1-x^2)/((1-x-x^2)(1-2x^2)). - _Paul Barry_, Jan 13 2005
%p A079284 with (combinat):a[0]:=0:a[1]:=1:a[2]:=1:for n from 2 to 50 do a[n]:=fibonacci(n-1)+2*a[n-2] od: seq(a[n], n=1..31); # _Zerinvary Lajos_, Mar 17 2008
%t A079284 CoefficientList[Series[(1 - x^2) / ((1 - x - x^2) (1 - 2 x^2)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 05 2013 *)
%t A079284 LinearRecurrence[{1,3,-2,-2},{1,1,3,4},40] (* _Harvey P. Dale_, Nov 30 2018 *)
%o A079284 (Magma) [Fibonacci(n+3)-2^Floor((n+1)/2): n in [0..40]]; // _Vincenzo Librandi_, Aug 05 2013
%Y A079284 Cf. A000045, A005672, A008949, A061667, A079284, A102517.
%K A079284 easy,nonn
%O A079284 0,3
%A A079284 _Paul Barry_, Feb 08 2003