A027077 a(n) = Sum_{k=n+1..2*n} T(n,k), T given by A027052.

1, 3, 8, 24, 71, 209, 612, 1784, 5189, 15081, 43838, 127528, 371395, 1082951, 3161866, 9243400, 27055153, 79280601, 232567194, 682905120, 2007104343, 5904004451, 17380510458, 51202600920, 150942696637, 445247984543

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Maple

T:= proc(n, k) option remember;
      if k<0 or k>2*n then 0
    elif k=0 or k=2 or k=2*n then 1
    elif k=1 then 0
    else add(T(n-1, k-j), j=1..3)
      fi
    end:
seq( add(T(n, k), k=n+1..2*n), n=1..30); # G. C. Greubel, Nov 06 2019

Mathematica

T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2 || k==2*n, 1, If[k==1, 0, Sum[T[n-1, k-j], {j, 3}]]]]; Table[Sum[T[n, k], {k, n+1, 2*n}], {n, 1, 30}] (* G. C. Greubel, Nov 06 2019 *)

Prog

(Sage)
@CachedFunction
def T(n, k):
    if (k<0 or k>2*n): return 0
    elif (k==0 or k==2 or k==2*n): return 1
    elif (k==1): return 0
    else: return sum(T(n-1, k-j) for j in (1..3))
[sum(T(n, k) for k in (n+1..2*n)) for n in (1..30)] # G. C. Greubel, Nov 06 2019

Crossrefs

Sequence in context: A291613 A238126 A079121 * A291243 A153774 A052855

Adjacent sequences: A027074 A027075 A027076 * A027078 A027079 A027080

Keyword

nonn

Author

Clark Kimberling

Extensions

Offset changed by G. C. Greubel, Nov 06 2019

Status

approved