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%I #19 Sep 08 2022 08:45:08
%S 1,3,9,24,61,149,354,823,1881,4240,9449,20857,45666,99291,214589,
%T 461336,987221,2103917,4467394,9454895,19951601,41989408,88155409,
%U 184670769,386072386,805624179,1678235829,3490492968,7249103581,15034563845
%N Diagonal sums of triangle A055249.
%H Vincenzo Librandi, <a href="/A079282/b079282.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,0,4).
%F a(n) = sum(sum((k+1)binomial(n-j, n-2j-k), k, 0, n-2j), j, 0, floor(n/2))
%F a(n) = (n-1)*2^n + F(n+3), with F(n) = A000045(n). - _Ralf Stephan_, May 09 2004
%F G.f.: (1-x)^2 / ((1-2*x)^2 * (1-x-x^2)). [_Joerg Arndt_, Aug 05 2013]
%t Table[(n - 1) 2^n + Fibonacci[n + 3], {n, 0, 30}] (* _Vincenzo Librandi_, Aug 05 2013 *)
%t LinearRecurrence[{5,-7,0,4},{1,3,9,24},30] (* _Harvey P. Dale_, May 29 2021 *)
%o (Magma) [(n-1)*2^n + Fibonacci(n+3): n in [0..30]]; // _Vincenzo Librandi_, Aug 05 2013
%Y Cf. A055249.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Feb 08 2003
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