A042414 -id:A042414 - cp's OEIS frontend

A042415 Denominators of continued fraction convergents to sqrt(735).

1, 9, 487, 4392, 237655, 2143287, 115975153, 1045919664, 56595637009, 510406652745, 27618554885239, 249077400619896, 13477798188359623, 121549261095856503, 6577137897364610785, 59315790337377353568, 3209629816115741703457

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,488,0,-1).

Cf. A042414, A040707.

Denominator[Convergents[Sqrt[735], 20]] (* Harvey P. Dale, Oct 11 2011 *)
CoefficientList[Series[(1 + 9 x - x^2)/(x^4 - 488 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 21 2014 *)

G.f.: -(x^2-9*x-1) / (x^4-488*x^2+1). - Colin Barker, Dec 12 2013

More terms from Colin Barker, Dec 12 2013

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}.

Original entry on oeis.org

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

Clark Kimberling

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).

Cf. A042413, A042414.

[(3*n^2+5*n-6) div 8: n in [1..70]]; // Vincenzo Librandi, Dec 11 2015

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

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 *)

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

a(n) = (3*n^2 + 5*n - 6)\8; \\ Altug Alkan, Dec 10 2015

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)

More terms from Michael De Vlieger, Dec 10 2015

cp's OEIS Frontend

A042415 Denominators of continued fraction convergents to sqrt(735).

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