OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
FORMULA
Empirical G.f.: x*(1+3*x+x^2)/(1-4*x^2+4*x^4). - Colin Barker, Jan 03 2012
Conjecture: a(n) = (6*r*n+(1+3*(1-r)*n)*(1-(-1)^n))*r^(n-1)/8, where r=sqrt(2). - Bruno Berselli, Jan 03 2011
EXAMPLE
Let esf abbreviate "elementary symmetric function". Then
0th esf of {1}: 1
1st esf of {1,2}: 1+2=3
2nd esf of {1,2,1} is 1*2+1*1+2*1=5
MATHEMATICA
f[k_] := 1 + Mod[k + 1, 2];
t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 33}] (* A203150 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Dec 29 2011
STATUS
approved