A203164 (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (4,1,2,3,4,1,2,3,...).

1, 5, 14, 50, 224, 320, 736, 2400, 10176, 12480, 27264, 86400, 359424, 414720, 884736, 2764800, 11390976, 12718080, 26763264, 82944000, 339738624, 371589120, 775028736, 2388787200, 9746251776, 10510663680, 21785739264, 66886041600

Offset

1,2

Links

Table of n, a(n) for n=1..28.

Formula

Conjecture: a(n)=48*a(n-4)-576*a(n-8) with G.f. x*(1+5*x+14*x^2+50*x^3+176*x^4+80*x^5+64*x^6) / (-1+24*x^4)^2. - R. J. Mathar, Oct 15 2013

Mathematica

f[k_] := 1 + Mod[k + 2, 4];
t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 33}] (* A203164 *)

Crossrefs

Cf. A010883, A203162, A203163, A203165.

Sequence in context: A272147 A272223 A107242 * A063835 A054664 A091218

Adjacent sequences: A203161 A203162 A203163 * A203165 A203166 A203167

Keyword

nonn

Author

Clark Kimberling, Dec 30 2011

Status

approved