A203150 (n-1)-st elementary symmetric function of the first n terms of (1,2,1,2,1,2,1,2,1,2,...)=A000034.

1, 3, 5, 12, 16, 36, 44, 96, 112, 240, 272, 576, 640, 1344, 1472, 3072, 3328, 6912, 7424, 15360, 16384, 33792, 35840, 73728, 77824, 159744, 167936, 344064, 360448, 737280, 770048, 1572864, 1638400, 3342336, 3473408, 7077888, 7340032

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

Cf. A000034, A167667 (bisection?), A053220 (bisection?)

Sequence in context: A213036 A032438 A025083 * A237351 A299490 A361274

Adjacent sequences: A203147 A203148 A203149 * A203151 A203152 A203153

Keyword

nonn,easy

Author

Clark Kimberling, Dec 29 2011

Status

approved