A026556 - OEIS

%I #7 Dec 17 2021 20:55:58

%S 1,3,8,24,52,156,319,954,1910,5696,11304,33648,66514,197778,390266,

%T 1159844,2286996,6795576,13397075,39809076,78489235,233262931,

%U 460030947,1367463642,2697786052,8021305890,15830906756,47082494816

%N a(n) = T(n, n-3), T given by A026552. Also a(n) = number of integer strings s(0), ..., s(n) counted by T, such that s(n) = 3.

%H G. C. Greubel, <a href="/A026556/b026556.txt">Table of n, a(n) for n = 3..1000</a>

%F a(n) = A026552(n, n-3).

%t T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+2)/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=A026552 *)

%t Table[T[n,n-3], {n,3,40}] (* _G. C. Greubel_, Dec 17 2021 *)

%o (Sage)

%o @CachedFunction

%o def T(n,k): # T = A026552

%o     if (k==0 or k==2*n): return 1

%o     elif (k==1 or k==2*n-1): return (n+2)//2

%o     elif (n%2==0): return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)

%o     else: return T(n-1, k) + T(n-1, k-2)

%o [T(n,n-3) for n in (3..40)] # _G. C. Greubel_, Dec 17 2021

%Y Cf. A026552, A026553, A026554, A026555, A026557, A026558, A026559, A026560, A026563, A026563, A026566, A026567, A027272, A027273, A027274, A027275, A027276.

%K nonn

%O 3,2

%A _Clark Kimberling_