A027070 a(n) = diagonal sum of right-justified array T given by A027052.

1, 1, 1, 4, 6, 12, 31, 73, 183, 476, 1248, 3322, 8943, 24271, 66355, 182538, 504824, 1402682, 3913585, 10959499, 30792445, 86775340, 245204312, 694603032, 1972115945, 5610955925, 15994866669, 45677496204, 130661330526, 374339736820, 1074025873959, 3085699969569, 8876601230175

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..750

Formula

a(n) = Sum_{k=0..n} A027052(n-k, 2*n-3*k). - Sean A. Irvine, Oct 22 2019

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, 2*n-3*k), k=0..n), n=0..35); # 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[Sum[T[n-k, 2*n-3*k], {k, 0, n}], {n, 0, 35}] (* 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))
[sum(T(n-k, 2*n-3*k) for k in (0..n)) for n in (0..35)] # G. C. Greubel, Nov 06 2019

Crossrefs

Sequence in context: A102043 A025017 A133427 * A087785 A366772 A081198

Adjacent sequences: A027067 A027068 A027069 * A027071 A027072 A027073

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 22 2019

Status

approved