A024204 [ (3rd elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+2 odd positive integers}.

0, 2, 4, 6, 10, 14, 19, 24, 30, 37, 44, 53, 61, 71, 81, 92, 103, 115, 128, 141, 156, 170, 186, 202, 219, 236, 254, 273, 292, 313, 333, 355, 377, 400, 423, 447, 472, 497, 524, 550, 578, 606, 635, 664, 694, 725, 756, 789, 821, 855, 889, 924, 959, 995, 1032

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,1,-2,1).

Formula

a(n) = floor((n^4 + 5*n^3 + 7*n^2 + 2*n)/(3*n^2 + 11*n + 9)). - Neven Juric (neven.juric(AT)apis-it.hr), neven.juric(AT)apis-it.hr, May 17 2007

a(n) = floor((n^3 + 2*n^2)/(3*n + 2)). - Gary Detlefs, Jul 13 2010

G.f.: x^2*(x^11-2*x^10+2*x^9-x^8-x^7-x^5-2*x^3-2) / ((x-1)^3*(x^2+x+1)*(x^6+x^3+1)). - Colin Barker, Aug 16 2014

For k > 0, a(9*k) = 27*k^2 + 4*k - 1, a(9*k+1) = 27*k^2 + 10*k, a(9*k+2) = 27*k^2 + 16*k + 1, a(9*k+3) = 27*k^2 + 22*k + 4, a(9*k+4) = 27*k^2 + 28*k + 6, a(9*k+5) = 27*k^2 + 34*k + 10, a(9*k+6) = 27*k^2 + 40*k + 14, a(9*k+7) = 27*k^2 + 46*k + 19, a(9*k+8) = 27*k^2 + 52*k + 24. - Jinyuan Wang, Jul 09 2020

Prog

(PARI) a(n) = (n^3+2*n^2)\(3*n+2) \\ Michel Marcus, Aug 16 2014

Crossrefs

Sequence in context: A098380 A007782 A035501 * A036641 A260732 A062425

Adjacent sequences: A024201 A024202 A024203 * A024205 A024206 A024207

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Michel Marcus, Aug 16 2014

Status

approved