A024224 a(n) = floor((4th elementary symmetric function of S(n))/(3rd elementary symmetric function of S(n))), where S(n) = {first n+3 positive integers congruent to 1 mod 3}.

0, 2, 4, 7, 11, 16, 22, 28, 35, 43, 51, 60, 70, 81, 93, 105, 118, 132, 146, 161, 177, 194, 212, 230, 249, 269, 289, 310, 332, 355, 379, 403, 428, 454, 480, 507, 535, 564, 594, 624, 655, 687, 719, 752, 786, 821, 857, 893, 930, 968, 1006, 1045, 1085, 1126, 1168, 1210, 1253, 1297, 1341, 1386, 1432

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-4,4,-4,4,-3,1).

Formula

G.f.: x^2*(2-2*x+3*x^2-2*x^3+3*x^4-2*x^5+2*x^6-x^7) / ((1-x)^3*(1+x^2)*(1+x^4)). - Colin Barker, Dec 10 2015

From Robert Israel, Dec 10 2015: (Start)

a(n) = floor(A024214(n+1)/A024213(n+1)).

a(n) = floor((3 n^2 + 5 n - 6)/8).

a(8*k+j) = 24*k^2 + (5 + 6*j) k + b(j), where b(j) = -1,0,2,4,7,11,16,22 for j = 0..7. (End)

Maple

seq(floor((3*n^2 + 5*n - 6)/8), n=1..100); # Robert Israel, Dec 10 2015

Mathematica

S[n_] := 3 Range[0, n + 2] + 1; Table[Floor[SymmetricPolynomial[4, S@ n]/SymmetricPolynomial[3, S@ n]], {n, 61}] (* Michael De Vlieger, Dec 10 2015 *)

Prog

(PARI) concat(0, Vec(x^2*(2-2*x+3*x^2-2*x^3+3*x^4-2*x^5+2*x^6-x^7)/((1-x)^3*(1+x^2)*(1+x^4)) + O(x^100))) \\ Colin Barker, Dec 10 2015
(PARI) a(n) = (3*n^2 + 5*n - 6)\8; \\ Altug Alkan, Dec 10 2015
(Magma) [(3*n^2+5*n-6) div 8: n in [1..70]]; // Vincenzo Librandi, Dec 11 2015

Crossrefs

Cf. A042413, A042414.

Sequence in context: A005311 A296202 A126613 * A025727 A319159 A025702

Adjacent sequences: A024221 A024222 A024223 * A024225 A024226 A024227

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

More terms from Michael De Vlieger, Dec 10 2015

Status

approved