A027037 Diagonal sum of left-justified array T given by A027023.

1, 1, 2, 3, 3, 6, 7, 11, 16, 21, 33, 48, 65, 101, 146, 203, 311, 450, 635, 963, 1396, 1989, 2993, 4348, 6233, 9329, 13574, 19543, 29135, 42446, 61303, 91123, 132884, 192377, 285309, 416384, 603925, 894069, 1305618, 1896495, 2803611, 4096182, 5957183, 8796287

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..n} A027023(n-k, k). - Sean A. Irvine, Oct 22 2019

Maple

T:= proc(n, k) option remember;
      if n<0 or k>2*n then 0
    elif 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, k), k=0..n), n=0..30); # G. C. Greubel, Nov 05 2019

Mathematica

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

Prog

(Sage)
@CachedFunction
def T(n, k):
    if (n<0 or k>2*n): return 0
    elif (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, k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Nov 05 2019

Crossrefs

Sequence in context: A028249 A121833 A091606 * A276428 A020878 A158278

Adjacent sequences: A027034 A027035 A027036 * A027038 A027039 A027040

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 21 2019

Status

approved