cp's OEIS Frontend

A026548 a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A026536.

%I A026548 #14 Apr 13 2022 01:15:35
%S A026548 1,1,4,7,22,42,127,249,746,1476,4414,8766,26215,52158,156041,310799,
%T A026548 930194,1854072,5550976,11070000,33152042,66139316,198115526,
%U A026548 395368914,1184511095,2364457980,7084871668,14145343660,42390336619
%N A026548 a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A026536.
%H A026548 G. C. Greubel, <a href="/A026548/b026548.txt">Table of n, a(n) for n = 0..1000</a>
%F A026548 a(n) = Sum_{k=0..n} A026536(n, k).
%t A026548 T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1,  Floor[n/2],
%t A026548 If[EvenQ[n], T[n-1,k-2] +T[n-1,k-1] +T[n-1,k], T[n-1, k-2] +T[n-1,k]]]];
%t A026548 Table[Sum[T[n, k], {k,0,n}], {n,0,40}] (* _G. C. Greubel_, Apr 12 2022 *)
%o A026548 (SageMath)
%o A026548 @CachedFunction
%o A026548 def T(n, k): # A026536
%o A026548     if k == 0 or k == 2*n: return 1
%o A026548     elif k == 1 or k == 2*n-1: return n//2
%o A026548     elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k)
%o A026548     return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
%o A026548 def A026548(n): return sum(T(n,k) for k in (0..n))
%o A026548 [A026548(n) for n in (0..40)] # _G. C. Greubel_, Apr 12 2022
%Y A026548 Cf. A026536, A026550, A027271.
%K A026548 nonn
%O A026548 0,3
%A A026548 _Clark Kimberling_
%E A026548 Missing a(0)=1 inserted by _Sean A. Irvine_, Oct 06 2019