A122452 Row sums of pendular triangle A122445.

1, 1, 3, 9, 32, 118, 455, 1803, 7304, 30104, 125834, 532154, 2272728, 9788310, 42464315, 185394551, 813950824, 3591328136, 15916173734, 70819784774, 316254424144, 1416906860412, 6367136425862, 28690381745294

Offset

0,3

Links

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

Maple

T := proc(n, k) option remember;
if k=0 and n=0 then 1;
elif k<0 or 2*(n-1)<k then 0;
elif n=2 and k<3 then 1;
else T(n-1, k) + `if`(k<n, T(n, 2*n-k-1), T(n-1, k) + T(n, 2*n-k-2));
end if; end proc;
seq( add(T(n, k), k = 0..2*n), n = 0..30); # G. C. Greubel, Mar 17 2021

Mathematica

T[n_, k_]:= T[n, k]= If[n==0 && k==0, 1, If[k<0 || k>2*(n-1), 0, If[n==2 && k<3, 1, T[n-1, k] + If[k<n, T[n, 2*n-k-1], T[n-1, k] + T[n, 2*n-k-2]]]]];
Table[Sum[T[n, k], {k, 0, 2*n}], {n, 0, 30}] (* G. C. Greubel, Mar 17 2021 *)

Prog

(Sage)
@CachedFunction
def T(n, k):
    if (n==0 and k==0): return 1
    elif (k<0 or k>2*(n-1)): return 0
    elif (n==2 and k<3): return 1
    else: return T(n-1, k) + ( T(n, 2*n-k-1) if k<n else T(n-1, k) + T(n, 2*n-k-2) )
[sum(T(n, k) for k in (0..2*n)) for n in (0..30)] # G. C. Greubel, Mar 17 2021

Crossrefs

Cf. A122445, A122446, A122447, A122448, A122449, A122450, A122451.

Sequence in context: A148985 A148986 A052872 * A192206 A091841 A063020

Adjacent sequences: A122449 A122450 A122451 * A122453 A122454 A122455

Keyword

nonn

Author

Paul D. Hanna, Sep 07 2006

Status

approved