A027045 a(n) = Sum_{k=n+1..2*n} T(n, k), T given by A027023.

1, 4, 11, 34, 103, 306, 901, 2636, 7685, 22372, 65111, 189590, 552547, 1612154, 4709369, 13773368, 40329465, 118217992, 346891115, 1018872626, 2995250535, 8812601062, 25948130525, 76456539156, 225427875325, 665066293480

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<3 or k=2*n then 1
    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 04 2019

Mathematica

T[n_, k_]:= T[n, k]= If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j, 3}]]; Table[Sum[T[n, k], {k, n+1, 2*n}], {n, 30}] (* G. C. Greubel, Nov 04 2019 *)

Prog

(Sage)
@CachedFunction
def T(n, k):
    if (k<3 or k==2*n): return 1
    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 04 2019
(Magma) function T(n, k)
  if k lt 3 or k eq 2*n then return 1;
  else return (&+[T(n-1, k-j): j in [1..3]]);
  end if; return T; end function;
[(&+[T(n, k): k in [n+1..2*n]]): n in [1..15]]; // G. C. Greubel, Nov 20 2019

Crossrefs

Cf. A027023.

Sequence in context: A144791 A180305 A060925 * A243781 A227329 A006765

Adjacent sequences: A027042 A027043 A027044 * A027046 A027047 A027048

Keyword

nonn

Author

Clark Kimberling

Extensions

Offset changed by G. C. Greubel, Nov 04 2019

Status

approved