cp's OEIS Frontend

A026526 a(n) = T(2n,n-1), T given by A026519.

%I A026526 #10 Dec 21 2021 02:34:14
%S A026526 1,2,9,32,130,516,2107,8632,35703,148390,619850,2598960,10933507,
%T A026526 46124274,195055005,826617216,3509650697,14926011714,63572290247,
%U A026526 271125967840,1157705297385,4948808238110,21175676836110,90692557152240,388751132082600,1667665994149376,7159105163384127,30753762496639504
%N A026526 a(n) = T(2n,n-1), T given by A026519.
%H A026526 G. C. Greubel, <a href="/A026526/b026526.txt">Table of n, a(n) for n = 1..1000</a>
%F A026526 a(n) = A026519(2*n, n-1).
%F A026526 a(n) = A026536(2*n, n-1).
%t A026526 T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+1)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k], T[n-1, k-1] + T[n-1, k-2] + T[n-1, k] ]]]]; (* T = A026519 *)
%t A026526 a[n_] := a[n] = Block[{$RecursionLimit = Infinity}, T[2*n, n-1] ];
%t A026526 Table[a[n], {n,40}] (* _G. C. Greubel_, Dec 20 2021 *)
%o A026526 (Sage)
%o A026526 @CachedFunction
%o A026526 def T(n,k): # T = A026519
%o A026526     if (k<0 or k>2*n): return 0
%o A026526     elif (k==0 or k==2*n): return 1
%o A026526     elif (k==1 or k==2*n-1): return (n+1)//2
%o A026526     elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
%o A026526     else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
%o A026526 [T(2*n,n-1) for n in (1..40)] # _G. C. Greubel_, Dec 20 2021
%Y A026526 Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026525, A026527, A026528, A026529, A026530, A026531, A026533, A026534, A027262, A027263, A027264, A027265, A027266.
%Y A026526 Cf. A026536.
%K A026526 nonn
%O A026526 1,2
%A A026526 _Clark Kimberling_
%E A026526 Terms a(20) onward added by _G. C. Greubel_, Dec 20 2021