A024212 2nd elementary symmetric function of first n+1 positive integers congruent to 1 mod 3.

4, 39, 159, 445, 1005, 1974, 3514, 5814, 9090, 13585, 19569, 27339, 37219, 49560, 64740, 83164, 105264, 131499, 162355, 198345, 240009, 287914, 342654, 404850, 475150, 554229, 642789, 741559, 851295, 972780, 1106824, 1254264, 1415964, 1592815, 1785735

Offset

1,1

Links

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

Wolfdieter Lang, On Generating functions of Diagonals Sequences of Sheffer and Riordan Number Triangles, arXiv:1708.01421 [math.NT], August 2017.

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

Formula

a(n) = n*(n+1)*(9*n^2+9*n-2)/8.

From Clark Kimberling, Aug 18 2012: (Start)

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5).

G.f.: (4 + 19*x + 4*x^2)/(1 - x)^5. (End)

From Wolfdieter Lang, Jul 30 2017: (Start)

E.g.f.: exp(x)*x*(32+124*x+72*x^2+9*x^3)/8 = exp(x)*x*(2 + x)*(16 + 54*x + 9*x^2)/8.

a(n) = A286718(n+1, n-1), n >= 1. (End)

Sum_{n>=1} 1/a(n) = 14 + 12*Pi*tan(sqrt(17)*Pi/6)/sqrt(17). - Amiram Eldar, Jul 10 2026

Mathematica

Table[n(n+1)(9n^2+9n-2)/8, {n, 40}] (* Harvey P. Dale, Oct 16 2023 *)
(* Alternative: *)
LinearRecurrence[{5, -10, 10, -5, 1}, {4, 39, 159, 445, 1005}, 40] (* Harvey P. Dale, Oct 16 2023 *)

Prog

(Magma) [n*(n+1)*(9*n^2+9*n-2)/8: n in [1..40]]; // Vincenzo Librandi, Oct 10 2011

Crossrefs

Cf. A016777, A286718.

Sequence in context: A297736 A286359 A201740 * A006408 A112460 A296594

Adjacent sequences: A024209 A024210 A024211 * A024213 A024214 A024215

Keyword

nonn,easy,changed

Author

Clark Kimberling

Status

approved