A106585 Triangle read by rows: even-numbered rows of A106580.

1, 1, 2, 2, 1, 2, 5, 7, 7, 1, 2, 5, 13, 22, 29, 29, 1, 2, 5, 13, 34, 65, 101, 130, 130, 1, 2, 5, 13, 34, 89, 185, 322, 481, 611, 611, 1, 2, 5, 13, 34, 89, 233, 514, 973, 1613, 2354, 2965, 2965, 1, 2, 5, 13, 34, 89, 233, 610, 1405, 2837, 5090, 8185, 11761, 14726, 14726

Offset

0,3

Links

G. C. Greubel, Rows n = 0..50 of the irregular triangle, flattened

Formula

T(n, k) = A106580(2*n, k).

Example

Irregular triangle begins as:
  1;
  1, 2, 2;
  1, 2, 5,  7,  7;
  1, 2, 5, 13, 22, 29,  29;
  1, 2, 5, 13, 34, 65, 101, 130,  130;
  1, 2, 5, 13, 34, 89, 185, 322,  481,  611,  611;
  1, 2, 5, 13, 34, 89, 233, 514,  973, 1613, 2354, 2965, 2965;
  1, 2, 5, 13, 34, 89, 233, 610, 1405, 2837, 5090, 8185, 11761, 14726, 14726;

Maple

A106580:= proc(n, k) option remember; if k =0 then 1; else A106580(n, k-1) + add(A106580(n-2*i, k-i), i=1..min(k, floor(n/2), n-k)); fi; end: for n from 0 to 18 by 2 do for k from 0 to n do printf("%d, ", A106580(n, k)); od; od; # R. J. Mathar, Aug 10 2007

Mathematica

T[n_, k_]:= T[n, k]= If[k==0, 1, T[n, k-1] + Sum[T[n-2*j, k-j], {j, 1, Min[k, Floor[n/2], n-k]}]];  (* T(n, k) = A106580; T(2*n, k) = A106585 *)
Table[T[2*n, k], {n, 0, 12}, {k, 0, 2*n}]//Flatten (* G. C. Greubel, Sep 07 2021 *)

Prog

(Sage)
@CachedFunction
def T(n, k): # T(n, k) = A106580; T(2*n, k) = A106585
    if (k<0): return 0
    elif (k==0): return 1
    else: return T(n, k-1) + sum( T(n-2*j, k-j) for j in (1..min(k, n//2, n-k)))
flatten([[T(2*n, k) for k in (0..2*n)] for n in (0..10)]) # G. C. Greubel, Sep 07 2021

Crossrefs

Cf. A106580, A106595.

Sequence in context: A183760 A125678 A091562 * A057227 A335190 A283170

Adjacent sequences: A106582 A106583 A106584 * A106586 A106587 A106588

Keyword

nonn,tabf,easy

Author

N. J. A. Sloane, May 30 2005

Extensions

More terms from R. J. Mathar, Aug 10 2007

Status

approved