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A026636 a(n) = Sum_{k=0..floor(n/2)} A026626(n-k, k).

%I A026636 #12 Feb 22 2025 22:30:57
%S A026636 1,1,2,4,6,11,17,30,47,78,125,205,330,536,866,1404,2270,3675,5945,
%T A026636 9622,15567,25190,40757,65949,106706,172656,279362,452020,731382,
%U A026636 1183403,1914785,3098190,5012975,8111166,13124141,21235309
%N A026636 a(n) = Sum_{k=0..floor(n/2)} A026626(n-k, k).
%H A026636 G. C. Greubel, <a href="/A026636/b026636.txt">Table of n, a(n) for n = 0..1000</a>
%H A026636 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,1,-1,-1).
%F A026636 G.f.: (1 + x^3 - x^4 + x^5 + x^7)/((1-x^4)*(1-x-x^2)).
%F A026636 From _G. C. Greubel_, Jun 21 2024: (Start)
%F A026636 a(n) = (1/20)*(2*LucasL(n-1) + 70*Fibonacci(n-1) - 15*(1+(-1)^n) - 4*cos((n-1)*Pi/2) - 2*sin((n-1)*Pi/2)) - [n=0] + [n=1].
%F A026636 E.g.f.: (1/10)*(cos(x) - 2*sin(x) - 15*cosh(x) - 10*(1 - x) + 2*exp(x/2)*(17*cosh(sqrt(5)*x/2) - 3*sqrt(5)*sinh(sqrt(5)*x/2))). (End)
%t A026636 LinearRecurrence[{1,1,0,1,-1,-1}, {1,1,2,4,6,11,17,30}, 41] (* _G. C. Greubel_, Jun 21 2024 *)
%o A026636 (Magma) I:=[2,4,6,11,17,30]; [1,1] cat [n le 6 select I[n] else Self(n-1) +Self(n-2) +Self(n-4) -Self(n-5) -Self(n-6): n in [1..50]]; // _G. C. Greubel_, Jun 21 2024
%o A026636 (SageMath)
%o A026636 @CachedFunction
%o A026636 def a(n): # a = A026636
%o A026636     if n<8: return (1,1,2,4,6,11,17,30)[n]
%o A026636     else: return a(n-1) +a(n-2) +a(n-4) -a(n-5) -a(n-6)
%o A026636 [a(n) for n in range(41)] # _G. C. Greubel_, Jun 21 2024
%Y A026636 Cf. A026626, A026627, A026628, A026629, A026630, A026631, A026632.
%Y A026636 Cf. A026633, A026634, A026635, A026961, A026962, A026963, A026964.
%Y A026636 Cf. A026965.
%K A026636 nonn,easy
%O A026636 0,3
%A A026636 _Clark Kimberling_