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A024174
a(n) is floor((4th elementary symmetric function of 1,2,..,n)/(3rd elementary symmetric function of 1,2,...,n)).
1
0, 0, 1, 2, 3, 4, 6, 8, 10, 13, 16, 19, 22, 25, 29, 33, 37, 42, 47, 52, 57, 62, 68, 74, 80, 87, 94, 101, 108, 115, 123, 131, 139, 148, 157, 166, 175, 184, 194, 204, 214, 225, 236, 247, 258, 269, 281, 293, 305, 318, 331, 344, 357, 370, 384, 398, 412, 427, 442
OFFSET
3,4
LINKS
FORMULA
Empirical g.f.: x^5*(x^7-2*x^6+2*x^5-2*x^4+x^3-x^2+x-1) / ((x-1)^3*(x^2+1)*(x^4+1)). - Colin Barker, Aug 16 2014
a(n) = floor( A000915(n-3)/A001303(n-2) ). - R. J. Mathar, Sep 23 2016
a(n) = floor((n - 3)*(15n^3 + 15n^2 - 10n - 8)/(120*n*(n + 1))). - Ivan Neretin, Nov 25 2016
a(n) = floor((A000217(n-2)/2 - 1)/2) = floor((n^2 - 3*n - 2)/8), n >= 4. - Ralf Steiner, Oct 25 2021
EXAMPLE
G.f. = x^5 + 2*x^6 + 3*x^7 + 4*x^8 + 6*x^9 + 8*x^10 + 10*x^11 + 13*x^12 + ...
MATHEMATICA
Table[Floor[(n - 3) (15 n^3 + 15 n^2 - 10 n - 8)/(120 n (n + 1))], {n, 3, 45}] (* Ivan Neretin, Nov 25 2016 *)
Insert[Table[Floor[1/8 (-2 - 3 n + n^2)], {n, 4, 45}], 0, 1] (* Ralf Steiner, Oct 27 2021 *)
PROG
(PARI) {a(n) = if( n<4, 0, (n-3) * (15*n^3 + 15*n^2 - 10*n - 8) \ (120 * n * (n+1)))}; /* Michael Somos, Nov 25 2016 */
CROSSREFS
KEYWORD
nonn
EXTENSIONS
Offset set to 3 by R. J. Mathar, Sep 23 2016
STATUS
approved