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

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

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Last modified September 28 14:14 EDT 2022. Contains 357070 sequences. (Running on oeis4.)