A027081 a(n) = Sum_{k=0..2n-3} T(n,k) * T(n,k+3), with T given by A027052.

8, 56, 438, 3574, 29738, 249200, 2094902, 17648718, 148968822, 1259807224, 10674450652, 90618393250, 770728674864, 6567151658496, 56054864624310, 479267092351534, 4104271159315190, 35200977081482376, 302343415930398696, 2600408469332918538, 22394817457275426524

Offset

3,1

Links

G. C. Greubel, Table of n, a(n) for n = 3..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+3), k=0..2*n-3), n=3..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+3], {k, 0, 2*n-3}], {n, 3, 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+3) for k in (0..2*n-3)) for n in (3..30)] # G. C. Greubel, Nov 07 2019

Crossrefs

Sequence in context: A323699 A323700 A182430 * A093134 A001398 A251250

Adjacent sequences: A027078 A027079 A027080 * A027082 A027083 A027084

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 22 2019

Status

approved