A027067 a(n) = Sum_{k=n..2*n} T(n,k), T given by A027052.

1, 1, 4, 10, 27, 77, 220, 632, 1821, 5257, 15206, 44068, 127951, 372173, 1084382, 3164498, 9248241, 27064057, 79296978, 232597316, 682960523, 2007206245, 5904191878, 17380855190, 51203234981, 150943862857, 445250129556

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ 3^(n + 1/2) / sqrt(Pi*n). - Vaclav Kotesovec, Nov 06 2019

Maple

T:= proc(n, k) option remember;
      if 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..2*n), n=0..30); # G. C. Greubel, Nov 06 2019

Mathematica

T[n_, k_]:= T[n, k]= 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, 2*n}], {n, 0, 30}] (* G. C. Greubel, Nov 06 2019 *)

Prog

(Sage)
@CachedFunction
def T(n, k):
    if (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..2*n)) for n in (0..30)] # G. C. Greubel, Nov 06 2019

Crossrefs

Sequence in context: A052982 A108672 A000495 * A050262 A295208 A222453

Adjacent sequences: A027064 A027065 A027066 * A027068 A027069 A027070

Keyword

nonn

Author

Clark Kimberling

Status

approved