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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, 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 (list; graph; refs; listen; history; text; internal format)
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

AUTHOR

N. J. A. Sloane, Jan 21 2003

EXTENSIONS

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

STATUS

approved

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Last modified November 15 08:37 EST 2019. Contains 329144 sequences. (Running on oeis4.)