A026676 a(n) = T(n, floor(n/2)), T given by A026670.

1, 1, 3, 4, 11, 16, 43, 65, 173, 267, 707, 1105, 2917, 4597, 12111, 19196, 50503, 80380, 211263, 337284, 885831, 1417582, 3720995, 5965622, 15652239, 25130844, 65913927, 105954110, 277822147, 447015744, 1171853635, 1886996681

Offset

0,3

Comments

Also a(n) = T(n,m) + T(n,m+1) + ... + T(n,n), m=[ (n+1)/2 ], T given by A026736.

Links

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

Mathematica

T[n_, k_]:= T[n, k] = If[k==0 || k==n, 1, If[k==n-1, n, If[EvenQ[n] && k==(n-2)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k]]]]; Table[Sum[T[n, k], {k, Floor[(n+1)/2], n}], {n, 0, 40}] (* G. C. Greubel, Jul 19 2019 *)

Prog

(PARI) T(n, k) = if(k==n || k==0, 1, k==n-1, n, if((n%2)==0 && k==(n-2)/2, T(n-1, k-1) + T(n-2, k-1) + T(n-1, k), T(n-1, k-1) + T(n-1, k) ));
vector(20, n, n--; sum(k=(n+1)\2, n, T(n, k)) ) \\ G. C. Greubel, Jul 19 2019
(Sage)
@CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (k==n-1): return n
    elif (mod(n, 2)==0 and k==(n-2)/2): return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k)
    else: return T(n-1, k-1) + T(n-1, k)
[sum(T(n, k) for k in (floor((n+1)/2)..n)) for n in (0..40)] # G. C. Greubel, Jul 19 2019
(GAP)
T:= function(n, k)
    if k=0 or k=n then return 1;
    elif k=n-1 then return n;
    elif (n mod 2)=0 and k=Int((n-2)/2) then return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k);
    else return T(n-1, k-1) + T(n-1, k);
    fi;
  end;
List([0..20], n-> Sum([Int((n+1)/2)..n], k-> T(n, k) )); # G. C. Greubel, Jul 19 2019

Crossrefs

Cf. A026670, A026736.

Sequence in context: A127804 A027306 A239024 * A142870 A324552 A143680

Adjacent sequences: A026673 A026674 A026675 * A026677 A026678 A026679

Keyword

nonn

Author

Clark Kimberling

Status

approved