A024386 [ (3rd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+2 positive integers congruent to 1 mod 4}.

3, 29, 114, 310, 685, 1323, 2324, 3804, 5895, 8745, 12518, 17394, 23569, 31255, 40680, 52088, 65739, 81909, 100890, 122990, 148533, 177859, 211324, 249300, 292175, 340353, 394254, 454314, 520985, 594735, 676048, 765424, 863379, 970445, 1087170

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = n(n+1)(4n^2+8n-3)/6.

G.f.: x*(-3-14*x+x^2) / (x-1)^5 . - R. J. Mathar, Oct 08 2011

Mathematica

Table[n (n + 1) (4 n^2 + 8 n - 3) / 6, {n, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {3, 29, 114, 310, 685}, 60] (* Vincenzo Librandi, Aug 12 2018 *)

Prog

(Magma)[n*(n+1)*(4*n^2+8*n-3)/6: n in [1..60]]; // Vincenzo Librandi, Aug 12 2018
(PARI) a(n)=n*(n+1)*(4*n^2+8*n-3)/6 \\ Charles R Greathouse IV, Oct 21 2022

Crossrefs

Sequence in context: A100202 A094068 A084105 * A171355 A163854 A227046

Adjacent sequences: A024383 A024384 A024385 * A024387 A024388 A024389

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved