A027080 a(n) = Sum_{k=0..2n-2} T(n,k) * T(n,k+2), with T given by A027052.

2, 15, 100, 757, 5902, 46907, 377520, 3065809, 25078650, 206416795, 1708129244, 14202265321, 118585167502, 993915161547, 8358970631568, 70518298143329, 596590060985546, 5060232622624651, 43022268222676124, 366575545244139845, 3129747701356459022, 26771150349554898415

Offset

2,1

Links

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

Crossrefs

Sequence in context: A356578 A362768 A258390 * A208347 A293045 A081018

Adjacent sequences: A027077 A027078 A027079 * A027081 A027082 A027083

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 22 2019

Status

approved