A026733 a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026725.

1, 1, 3, 5, 13, 23, 57, 103, 249, 455, 1083, 1993, 4693, 8679, 20275, 37633, 87377, 162643, 375789, 701075, 1613413, 3015563, 6916957, 12948083, 29617161, 55513327, 126678893, 237705547, 541325021, 1016736115, 2311294377

Offset

0,3

Links

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

Formula

Conjecture: (-n+2)*a(n) +(n-2)*a(n-1) +2*(4*n-13)*a(n-2) +8*(-n+4)*a(n-3) +5*(-3*n+14)*a(n-4) +(15*n-94)*a(n-5) +2*(-2*n+9)*a(n-6) +4*(n-6)*a(n-7)=0. - R. J. Mathar, Oct 26 2019

Maple

A026733 := proc(n)
    add(A026725(n, k), k=0..floor(n/2)) ;
end proc:
seq(A026733(n), n=0..10) ; # R. J. Mathar, Oct 26 2019

Mathematica

T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[OddQ[n] && k==(n-1)/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, 0, Floor[n/2]}], {n, 0, 30}] (* G. C. Greubel, Oct 26 2019 *)

Prog

(PARI) T(n, k) = if(k==n || k==0, 1, if(2*k==n-1, T(n-1, k-1) + T(n-2, k-1) + T(n-1, k), T(n-1, k-1) + T(n-1, k) ));
vector(31, n, sum(k=0, floor(n-1/2), T(n-1, k)) ) \\ G. C. Greubel, Oct 26 2019
(Sage)
@CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n, 2)==1 and k==(n-1)/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 (0..floor(n/2))) for n in (0..30)] # G. C. Greubel, Oct 26 2019

Crossrefs

Sequence in context: A045414 A089067 A339888 * A005824 A336103 A027305

Adjacent sequences: A026730 A026731 A026732 * A026734 A026735 A026736

Keyword

nonn

Author

Clark Kimberling

Status

approved