A203165 (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (3,4,1,2,3,4,1,2,...).

1, 7, 19, 50, 174, 768, 1056, 2400, 7776, 32832, 39744, 86400, 273024, 1133568, 1299456, 2764800, 8626176, 35500032, 39481344, 82944000, 256794624, 1051066368, 1146617856, 2388787200, 7357464576, 30003167232, 32296402944, 66886041600

Offset

1,2

Links

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

Formula

Conjecture: G.f. x*(1+7*x+19*x^2+50*x^3+126*x^4+432*x^5+144*x^6) / (-1+24*x^4)^2 with a(n) = 48*a(n-4)-576*a(n-8). - R. J. Mathar, Jul 02 2013

Mathematica

f[k_] := 1 + Mod[k + 1, 4];
t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 33}]  (* A203165 *)

Crossrefs

Cf. A010883, A203162, A203163, A203164.

Sequence in context: A018728 A027523 A100545 * A332364 A100450 A155423

Adjacent sequences: A203162 A203163 A203164 * A203166 A203167 A203168

Keyword

nonn

Author

Clark Kimberling, Dec 30 2011

Status

approved