A027078 a(n) = Sum_{k=0..n} T(n,k) * T(n,n+k), with T given by A027052.

1, 0, 2, 8, 31, 130, 590, 2798, 13541, 66724, 332708, 1673536, 8479367, 43218034, 221383712, 1138976166, 5882112985, 30479772624, 158413903096, 825556260636, 4312814257059, 22580855859166, 118468635595680, 622698941708890

Offset

0,3

Links

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

Crossrefs

Sequence in context: A150793 A150794 A150795 * A150796 A150797 A150798

Adjacent sequences: A027075 A027076 A027077 * A027079 A027080 A027081

Keyword

nonn

Author

Clark Kimberling

Status

approved