A027079 a(n) = Sum_{k=0..2n-1} T(n,k) * T(n,k+1), with T given by A027052.

0, 4, 24, 160, 1136, 8420, 64224, 499984, 3952928, 31634724, 255682432, 2083562368, 17097573344, 141143273396, 1171240794072, 9763809318912, 81724975129664, 686539343850164

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)*T(n, k+1), k=0..2*n-1), n=1..30); # G. C. Greubel, Nov 07 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]*T[n, k+1], {k, 0, 2*n-1}], {n, 30}] (* G. C. Greubel, Nov 07 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)*T(n, k+1) for k in (0..2*n-1)) for n in (1..30)] # G. C. Greubel, Nov 07 2019

Crossrefs

Sequence in context: A059304 A069722 A343842 * A213441 A238299 A221656

Adjacent sequences: A027076 A027077 A027078 * A027080 A027081 A027082

Keyword

nonn

Author

Clark Kimberling

Status

approved