A079512 a(0)=1, a(1)=1; for n>1, a(n) = Sum_{i=0..n/2} binomial(n-i-1,i)*a(n-2i-1) + ((n+1) mod 2).

1, 1, 2, 3, 6, 13, 29, 72, 185, 499, 1414, 4132, 12554, 39332, 126815, 420769, 1430790, 4986139, 17772536, 64708212, 240482750, 911008926, 3515571177, 13807269626, 55147622607, 223864614364, 922952281744, 3862571220690, 16399630000144

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..925

S. Kitaev, Multi-avoidance of generalized patterns, Discrete Math., 260 (2003), 89-100.

Maple

with(combinat): a := array(0..50): a[0] := 1: a[1] := 1: for n from 2 to 50 do: a[n] := 0: for i from 0 to floor((n-1)/2.) do: a[n] := a[n]+binomial(n-i-1, i)*a[n-2*i-1]: od:a[n] := a[n]+((n+1) mod 2): od:seq(a[n], n=0..50);

Mathematica

a[0] = a[1] = 1; a[n_] := a[n] = Sum[ Binomial[n - i - 1, i]*a[n - 2i - 1], {i, 0, Floor[n/2]}] + Mod[n + 1, 2]; Table[a[n], {n, 0, 30}]

Prog

(PARI) {a(n) = sum(j=0, floor(n/2), binomial(n-j-1, j)*a(n-2*j-1)) + lift(Mod(n+1, 2))};
vector(30, n, n--; if(n==0 && n==1, 1, a(n))) \\ G. C. Greubel, Jan 17 2019

Crossrefs

Sequence in context: A032066 A107316 A124682 * A280746 A174191 A052937

Adjacent sequences: A079509 A079510 A079511 * A079513 A079514 A079515

Keyword

easy,nonn,changed

Author

N. J. A. Sloane, Jan 21 2003

Extensions

More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 22 2003

Status

approved