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A026676 a(n) = T(n, floor(n/2)), T given by A026670. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 18 18:09 EDT 2021. Contains 345120 sequences. (Running on oeis4.)