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A046162 Reduced numerators of (n-1)^2/(n^2+n+1). Arises in Routh's theorem. 3
0, 1, 4, 3, 16, 25, 12, 49, 64, 27, 100, 121, 48, 169, 196, 75, 256, 289, 108, 361, 400, 147, 484, 529, 192, 625, 676, 243, 784, 841, 300, 961, 1024, 363, 1156, 1225, 432, 1369, 1444, 507, 1600, 1681, 588, 1849, 1936, 675, 2116, 2209, 768, 2401, 2500 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

With offset 0, multiplicative with a(3^e) = 3^(2e-1), a(p^e) = p^(2e) otherwise. - David W. Wilson, Jun 12 2005, corrected by Robert Israel, Apr 28 2017

LINKS

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

Eric Weisstein's World of Mathematics, Routh's Theorem.

FORMULA

G.f.: x*(x^8+4*x^7+3*x^6+13*x^5+13*x^4+3*x^3+4*x^2+x)/(1-x^3)^3.

a(n) = (n-1)^2/3 if n-1 == 0 mod 3, (n-1)^2 otherwise. - David W. Wilson, Jun 12 2005, corrected by Robert Israel, Apr 28 2017

MAPLE

seq(numer((n-1)^2/(n^2+n+1)), n=1..51) ; # Zerinvary Lajos, Jun 04 2008

seq(denom(3/n^2-2), n=0..76) ; # Zerinvary Lajos, Jun 04 2008

CROSSREFS

Cf. A046163.

Sequence in context: A288067 A038233 A176737 * A060509 A113203 A034486

Adjacent sequences:  A046159 A046160 A046161 * A046163 A046164 A046165

KEYWORD

nonn,mult

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified December 12 07:31 EST 2019. Contains 329948 sequences. (Running on oeis4.)