A027038 Diagonal sum of right-justified array T given by A027023.

1, 1, 2, 5, 7, 18, 43, 103, 264, 687, 1809, 4836, 13049, 35493, 97218, 267857, 741791, 2063574, 5763595, 16155403, 45429488, 128121191, 362287433, 1026918632, 2917313257, 8304598593, 23685134746, 67669857661, 193652803391

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..n} T(n-k, 2*n-3*k), where T = A027023. - G. C. Greubel, Nov 05 2019

Maple

T:= proc(n, k) option remember;
      if k<3 or k=2*n then 1
    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..30); # G. C. Greubel, Nov 05 2019

Mathematica

T[n_, k_]:= T[n, k]= If[n<0, 0, If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j, 3}]]]; Table[Sum[T[n-k, 2*n-3*k], {k, 0, n}], {n, 0, 30}] (* G. C. Greubel, Nov 05 2019 *)

Prog

(Sage)
@CachedFunction
def T(n, k):
    if (k<3 or k==2*n): return 1
    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..30)] # G. C. Greubel, Nov 05 2019

Crossrefs

Sequence in context: A247323 A099357 A306918 * A341322 A173929 A173299

Adjacent sequences: A027035 A027036 A027037 * A027039 A027040 A027041

Keyword

nonn

Author

Clark Kimberling

Status

approved