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A026742 a(n) = T(n, floor(n/2)), T given by A026736. 1
1, 1, 2, 3, 6, 11, 21, 43, 79, 173, 309, 707, 1237, 2917, 5026, 12111, 20626, 50503, 85242, 211263, 354080, 885831, 1476368, 3720995, 6173634, 15652239, 25873744, 65913927, 108628550, 277822147, 456710589, 1171853635, 1922354351 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

a(n) ~ phi^(3*n/2 - (7 + (-1)^n)/4) / sqrt(5), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jul 19 2019

MATHEMATICA

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

PROG

(PARI) T(n, k) = if(k==n || k==0, 1, 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--; T(n, n\2)) \\ G. C. Greubel, Jul 19 2019

(Sage) @CachedFunction

def T(n, k):

    if (k==0 or k==n): return 1

    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)

[T(n, floor(n/2)) 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 (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;

Flat(List([0..20], n-> T(n, Int(n/2)) )); # G. C. Greubel, Jul 19 2019

CROSSREFS

Cf. A026736.

Sequence in context: A339151 A164362 A329667 * A316471 A018268 A082616

Adjacent sequences:  A026739 A026740 A026741 * A026743 A026744 A026745

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified December 1 13:38 EST 2021. Contains 349429 sequences. (Running on oeis4.)