A027056 a(n) = A027052(n, 2n-1).

0, 2, 4, 8, 18, 42, 102, 256, 658, 1722, 4570, 12264, 33212, 90626, 248892, 687360, 1907506, 5316266, 14873082, 41751944, 117567784, 331979650, 939807344, 2666718976, 7583071868, 21605822594, 61672362872, 176338826728, 505001067346, 1448365610778, 4159725843526, 11962301199744

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..750

Formula

Conjecture:b D-finite with recurrence (-n+1)*a(n) +2*(3*n-4)*a(n-1) +(-7*n+3)*a(n-2) +4*(-2*n+13)*a(n-3) +(5*n-29)*a(n-4) +2*(n-2)*a(n-5) +3*(n-5)*a(n-6)=0. - R. J. Mathar, Jun 15 2020

a(n) ~ 3^(n + 3/2) / (2 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Mar 08 2023

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( T(n, 2*n-1), n=1..30); # G. C. Greubel, Nov 06 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[T[n, 2*n-1], {n, 30}] (* G. C. Greubel, Nov 06 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))
[T(n, 2*n-1) for n in (1..30)] # G. C. Greubel, Nov 06 2019

Crossrefs

Sequence in context: A182780 A078678 A261492 * A024428 A330269 A049075

Adjacent sequences: A027053 A027054 A027055 * A027057 A027058 A027059

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 22 2019

Status

approved