

A114364


a(n) = n*(n+1)^2.


1



4, 18, 48, 100, 180, 294, 448, 648, 900, 1210, 1584, 2028, 2548, 3150, 3840, 4624, 5508, 6498, 7600, 8820, 10164, 11638, 13248, 15000, 16900, 18954, 21168, 23548, 26100, 28830, 31744, 34848, 38148, 41650, 45360, 49284, 53428, 57798, 62400
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OFFSET

1,1


COMMENTS

Former name was "Numbers k such that k*x^3 + x + 1 is not prime."
Theorem: y = k*x^3 + x + 1 is not prime for k = 4, 18, 48, ..., n*(n+1)^2. Proof: n*(n+1)^2*x^3 + x + 1 = ((n+1)*x + 1)*((n^2+n)*x^2  n*x + 1). Thus (n+1)*x + 1 divides y. This could possibly be used as a pretest for compositeness. This sequence is the same as beginning with the third term of A045991.


LINKS

Jinyuan Wang, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,6,4,1).


FORMULA

a(n) = n*(n+1)^2.
G.f.: 2 * (2 + x)/(1 + x)^4.  Michael De Vlieger, Feb 03 2019


MAPLE

seq(2*binomial(n, 2)*n, n=2..40); # Zerinvary Lajos, Apr 25 2007


MATHEMATICA

CoefficientList[Series[(2 (2 + x))/(1 + x)^4, {x, 0, 38}], x] (* or *)
Array[# (# + 1)^2 &, 39] (* Michael De Vlieger, Feb 03 2019 *)


PROG

(PARI) g2(n) = for(x=1, n, y=x*(x+1)^2; print1(y", "))


CROSSREFS

Cf. A045991.
Sequence in context: A254950 A213492 A163188 * A045991 A228108 A259451
Adjacent sequences: A114361 A114362 A114363 * A114365 A114366 A114367


KEYWORD

easy,nonn


AUTHOR

Cino Hilliard, Feb 09 2006


EXTENSIONS

Name changed by Jon E. Schoenfield, Feb 03 2019


STATUS

approved



