A024398 a(n) = [ (2nd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+1 positive integers congruent to 2 mod 3}.

0, 1, 4, 8, 14, 22, 31, 41, 53, 67, 82, 98, 116, 136, 157, 179, 203, 229, 256, 284, 314, 346, 379, 413, 449, 487, 526, 566, 608, 652, 697, 743, 791, 841, 892, 944, 998, 1054, 1111, 1169, 1229, 1291, 1354, 1418, 1484, 1552, 1621, 1691, 1763, 1837, 1912, 1988

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-3,1).

Formula

a(n) = (1/4)*(3*(n^2-n-1) - (-1)^floor(n/2)), n > 1. - Ralf Stephan, Jun 09 2005

G.f.: x^2*(-1-x-2*x^3+x^4) / ( (x^2+1)*(x-1)^3 ). - R. J. Mathar, Oct 08 2011

Mathematica

Join[{0}, LinearRecurrence[{3, -4, 4, -3, 1}, {1, 4, 8, 14, 22}, 60]] (* or *) Join[{0}, Table[(3 (n^2 - n - 1) - (-1)^(Floor[n/2]))/4, {n, 2, 55}]] (* Vincenzo Librandi, Aug 12 2018 *)

Prog

(Magma) [0] cat [(3*(n^2-n-1)-(-1)^(n div 2)) div 4: n in [2..60]]; // Vincenzo Librandi, Aug 12 2018

Crossrefs

Sequence in context: A337232 A004797 A053459 * A054347 A194149 A351362

Adjacent sequences: A024395 A024396 A024397 * A024399 A024400 A024401

Keyword

nonn

Author

Clark Kimberling

Status

approved