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A026757

a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026747.

1, 1, 2, 4, 6, 11, 20, 32, 58, 102, 169, 302, 527, 888, 1573, 2741, 4661, 8215, 14316, 24481, 43023, 74998, 128747, 225867, 393838, 678047, 1188201, 2072239, 3575728, 6261248, 10921278, 18879372, 33040083, 57637061

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OFFSET

0,3

LINKS

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

MAPLE

A026747 := proc(n, k) option remember;

if k=0 or k = n then 1;

elif type(n, 'even') and k <= n/2 then

procname(n-1, k-1)+procname(n-2, k-1)+procname(n-1, k) ;

else

procname(n-1, k-1)+procname(n-1, k) ;

end if ;

end proc:

seq(add(A026747(n-k, k), k=0..floor(n/2)), n=0..30); # G. C. Greubel, Oct 29 2019

MATHEMATICA

T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[EvenQ[n] && k<=n/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], {k, 0, Floor[n/2]}], {n, 0, 30}] (* G. C. Greubel, Oct 29 2019 *)

PROG

(SageMath)

@CachedFunction

def T(n, k):

if (k==0 or k==n): return 1

elif (mod(n, 2)==0 and k<=n/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, k) for k in (0..floor(n/2))) for n in (0..30)] # G. C. Greubel, Oct 29 2019

CROSSREFS

Cf. A026747, A026748, A026749, A026750, A026751, A026752, A026753, A026754, A026755, A026756.

Sequence in context: A018170 A113913 A002097 * A026385 A254532 A199926

Adjacent sequences: A026754 A026755 A026756 * A026758 A026759 A026760