0,3

Number of compositions of n with at least one even part (offset 2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 29 2004

First differences of A008466. a(n) = A008466(n+2) - A008466(n+1). - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 06 2006

a(n)=sum(sum(binomial(n-j, n-2j-k), k, 0, n-2j), j, 0, floor(n/2)) - Paul Barry (pbarry(AT)wit.ie), Feb 07 2003

Row sums of A091597. G.f.: x(1-x)/((1-2x)(1-x-x^2)); a(n)=2^(n+1)-Fib(n+2). - Paul Barry (pbarry(AT)wit.ie), Jan 23 2004

a(n)=sum{j=0..n, sum{k=0..n, binomial(n-k, k+j)}} - Paul Barry (pbarry(AT)wit.ie), Aug 29 2004

a(n) = (sum of (n+1)-th row of the triangle in A108617) / 2. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 12 2005

a(n) = 2^(n+1)-Fibonacci(n+2). - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 06 2006

a(n) = term (1,1) - term (2,2) in the 3x3 matrix [2,0,0; 0,1,1; 0,1,0]^n. - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 28 2008

a(n)=2^n-(1/2)*[1/2+(1/2)*sqrt(5)]^n-(1/10)*[1/2+(1/2)*sqrt(5)]^n*sqrt(5)+(1/10)*sqrt(5)*[1/2-(1 /2)*sqrt(5)]^n-(1/2)*[1/2-(1/2)*sqrt(5)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Oct 02 2008]

a := proc (n) local K; K := Matrix ([[2, 0, 0], [0, 1, 1], [0, 1, 0]])^n; K[1, 1]-K[2, 2]; end; seq (a(n), n=0..31); - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 28 2008

Row sums of triangle A131767. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 13 2007

a(n) = A101220(1, 2, n+1).

T(n, n) + T(n, n+1) + ... + T(n, 2n), T given by A027926.

Diagonal sums of A055248

Cf. A000045, A000079, A008466, A059570, A099036, A047967.

Sequence in context: A059776 A091360 A090764 this_sequence A134389 A111297 A077864

Adjacent sequences: A027931 A027932 A027933 this_sequence A027935 A027936 A027937

nonn

Clark Kimberling (ck6(AT)evansville.edu)

Simpler definition from Miklos Kristof (kristmikl(AT)freemail.hu), Nov 24 2003

Initial zero added by N. J. A. Sloane (njas(AT)research.att.com), Feb 13 2008