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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}. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A003682

Adjacent sequences:  A024395 A024396 A024397 * A024399 A024400 A024401

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified March 2 06:28 EST 2021. Contains 341742 sequences. (Running on oeis4.)