A027043 a(n) = Sum_{k=0..2n} (k+1) * A027023(n,k).

1, 6, 23, 80, 285, 990, 3367, 11256, 37097, 120862, 390123, 1249728, 3978365, 12598350, 39718403, 124743104, 390491505, 1218875302, 3794984883, 11789335464, 36551285573, 113120066678, 349523991123, 1078402178776

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..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((k+1)*T(n, k), k=0..2*n), n=0..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[(k+1)*T[n, k], {k, 0, 2*n}], {n, 0, 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((k+1)*T(n, k) for k in (0..2*n)) for n in (0..30)] # G. C. Greubel, Nov 04 2019

Crossrefs

Sequence in context: A114245 A220238 A078798 * A006815 A264690 A241394

Adjacent sequences: A027040 A027041 A027042 * A027044 A027045 A027046

Keyword

nonn

Author

Clark Kimberling

Status

approved