A094876 a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = 1; then a(n) = sum( a(2*i)*a(3*j)) where 1< = i< = n, 1< = j< = n and 2*i+3*j = n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 5, 2, 5, 5, 5, 5, 14, 5, 14, 14, 14, 14, 42, 14, 42, 42, 42, 42, 132, 42, 132, 132, 132, 132, 429, 132, 429, 429, 429, 429, 1430, 429, 1430, 1430, 1430, 1430, 4862, 1430, 4862, 4862, 4862, 4862, 16796, 4862, 16796, 16796

Offset

1,11

Links

Antti Karttunen, Table of n, a(n) for n = 1..1001

Formula

(a(n)) satisfies : a(k)=1 for 1<=k<=8 then for n>=1 a(6n+2)=a(6n+3)=a(6n+4)=a(6n+6); a(6n+5)=a(6n+7)=a(6*n+2)+A000245(n)

a(6n-1) = a(6n+1) = a(6n+2) = a(6n+3) = a(6n+4) = a(6n+6) = A000108(n) except a(-1) = 0; generating function = (1-sqrt(1-4x^6))(1+x^2+x^3+x^4+x^5+x^7)/(2x^7)-1/x. - Alec Mihailovs (alec(AT)mihailovs.com), Jun 16 2004

Maple

A094876:=proc(N) local n; if N<1 then 0 else n:=floor((N-1)/6)+`if`(N mod 6=5, 1, 0); binomial(2*n, n)/(n+1) fi end; seq(A094876(N), N=1..62);

Mathematica

Rest[CoefficientList[Series[(1-Sqrt[1-4x^6])(1+x^2+x^3+x^4+x^5+x^7)/ (2x^7)- 1/x, {x, 0, 70}], x]] (* Harvey P. Dale, Aug 29 2011 *)

Prog

(PARI) v=vector(90, j, 1); for(n=7, 90, A=sum(i=1, n, sum(j=1, n, if(2*i+3*j-n, 0, v[2*i]*v[3*j]))); v[n]=A); a(n)=v[n];

Crossrefs

Cf. A000108.

Sequence in context: A276058 A247302 A029252 * A144159 A318662 A073610

Adjacent sequences: A094873 A094874 A094875 * A094877 A094878 A094879

Keyword

nonn

Author

Benoit Cloitre, Jun 14 2004

Status

approved