A046162 -id:A046162 - cp's OEIS frontend

A147560 a(n) = 4*A046162(n+1).

0, 4, 16, 12, 64, 100, 48, 196, 256, 108, 400, 484, 192, 676, 784, 300, 1024, 1156, 432, 1444, 1600, 588, 1936, 2116, 768, 2500, 2704, 972, 3136, 3364, 1200, 3844, 4096, 1452, 4624, 4900, 1728, 5476, 5776, 2028, 6400, 6724, 2352, 7396, 7744, 2700, 8464

Offset: 0

Paul Curtz, Nov 07 2008

G. C. Greubel, Table of n, a(n) for n = 0..5000

Companion to A144437.
Cf. A046162.
Cf. A171522. [R. J. Mathar, Dec 15 2009]

[4*Numerator(n^2/(n^2+3*n+3)): n in [0..70]]; // G. C. Greubel, Oct 27 2022

A046162 := proc(n) (n-1)^2/(n^2+n+1) ; numer(%) ; end proc: A147560 := proc(n) 4*A046162(n+1) ; end proc: seq(A147560(n),n=0..70) ; # R. J. Mathar, Dec 15 2009

a[n_] := 4 * Numerator[n^2/(n^2 + 3*n + 3)]; Array[a, 50, 0] (* Amiram Eldar, Aug 14 2022 *)

[4*numerator(n^2/(n^2 +3*n +3)) for n in range(71)] # G. C. Greubel, Oct 27 2022

a(n) = 4*numerator(n^2/(n^2 + 3*n + 3)).
Sum_{n>=1} 1/a(n) = 11*Pi^2/216. - Amiram Eldar, Aug 14 2022
G.f.: 4*x*(1 + 4*x + 3*x^2 + 13*x^3 + 13*x^4 + 3*x^5 + 4*x^6 + x^7)/(1-x^3)^3. - G. C. Greubel, Oct 27 2022

More terms from R. J. Mathar, Dec 15 2009

A046163 Reduced denominators of (n-1)^2/(n^2 + n + 1).

Original entry on oeis.org

1, 7, 13, 7, 31, 43, 19, 73, 91, 37, 133, 157, 61, 211, 241, 91, 307, 343, 127, 421, 463, 169, 553, 601, 217, 703, 757, 271, 871, 931, 331, 1057, 1123, 397, 1261, 1333, 469, 1483, 1561, 547, 1723, 1807, 631, 1981, 2071, 721, 2257, 2353, 817, 2551, 2653

Offset: 1

Eric W. Weisstein

Arises in Routh's theorem.

G. C. Greubel, Table of n, a(n) for n = 1..5000
Eric Weisstein's World of Mathematics, Routh's Theorem.
Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).

Cf. A046162 (numerators).

[Denominator((n-1)^2/(n^2+n+1)): n in [1..70]]; // G. C. Greubel, Oct 27 2022

a[n_] := Denominator[(n - 1)^2/(n^2 + n + 1)]; Array[a, 50] (* Amiram Eldar, Aug 11 2022 *)

[denominator((n-1)^2/(n^2+n+1)) for n in range(1,71)] # G. C. Greubel, Oct 27 2022

G.f.: x*(1 + 7*x + 13*x^2 + 4*x^3 + 10*x^4 + 4*x^5 + x^6 + x^7 + x^8)/(1 - x^3)^3.
From Amiram Eldar, Aug 11 2022: (Start)
a(n) = numerator((n^2 + n + 1)/3).
Sum_{n>=1} 1/a(n) = (2*tanh(Pi/(2*sqrt(3))) + 3*tanh(sqrt(3)*Pi/2))*Pi/(3*sqrt(3)) - 1. (End)

cp's OEIS Frontend

A147560 a(n) = 4*A046162(n+1).

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