A027082 Irregular triangular array: T(n,0) = 1 for n >= 1; T(n,1) = T(n,2) = 1 for n >= 1; T(n,k) = T(n-1,k-3) + T(n-1,k-2) + T(n-1,k-1) for 3 <= k <= 2n-1 and n >= 2; and T(n,2n) = T(n-1,2n-3) + T(n-1,2n-2) for n >= 2.

1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 3, 5, 6, 5, 1, 1, 1, 3, 5, 9, 14, 16, 11, 1, 1, 1, 3, 5, 9, 17, 28, 39, 41, 27, 1, 1, 1, 3, 5, 9, 17, 31, 54, 84, 108, 107, 68, 1, 1, 1, 3, 5, 9, 17, 31, 57, 102, 169, 246, 299, 283, 175, 1, 1, 1, 3, 5, 9, 17, 31, 57

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• tabf

Examples

			The first 6 rows:
1
1 .. 1 .. 1
1 .. 1 .. 1 .. 3 .. 2
1 .. 1 .. 1 .. 3 .. 5 .. 6 .. 5
1 .. 1 .. 1 .. 3 .. 5 .. 9 .. 14 .. 16 .. 11
1 .. 1 .. 1 .. 3 .. 5 .. 9 .. 17 .. 28 .. 39 .. 41 .. 27
		

Links

• R. J. Mathar, Table of n, a(n) for n = 0..1000, recomputing the old b-file for offset 0.

Programs

Maple

A027082 := proc(n,k)
    option remember;
    if k < 0 or k > 2*n then
        0;
    elif k <=2 then
        1;
    elif k  = 2*n then
        procname(n-1,k-3)+procname(n-1,k-2) ;
    else
        procname(n-1,k-3)+procname(n-1,k-2)+procname(n-1,k-1) ;
    end if;
end proc:
seq(seq(A027082(n,k),k=0..2*n),n=0..10) ; # R. J. Mathar, Jun 24 2020

Mathematica

t[n_, 0] := 1; t[n_, 1] := 1; t[n_, 2] := 1; t[n_, k_] := t[n, k] = If[k < 2 n, t[n - 1, k - 3] + t[n - 1, k - 2] + t[n - 1, k - 1], t[n - 1, 2 n - 3] + t[n - 1, 2 n - 2]]; u = Table[t[n, k], {n, 0, 10}, {k, 0, 2 n}]; v = Flatten[u]  (* A027082 *)

Extensions

Corrected and edited by Clark Kimberling, Aug 06 2014

Offset corrected to 0 and b-file recomputed by R. J. Mathar, Jun 24 2020