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A268644 a(n) = 4*n^3 - 3*n^2 - 2*n - 1. 1
-1, -2, 15, 74, 199, 414, 743, 1210, 1839, 2654, 3679, 4938, 6455, 8254, 10359, 12794, 15583, 18750, 22319, 26314, 30759, 35678, 41095, 47034, 53519, 60574, 68223, 76490, 85399, 94974, 105239, 116218, 127935, 140414, 153679, 167754, 182663, 198430, 215079, 232634, 251119 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In general, the ordinary generating function for the values of cubic polynomial p*n^3 + q*n^2 + k*n + m is (m + (p + q + k - 3*m)*x + (4*p - 2*k + 3*m)*x^2 + (p - q + k - m)*x^3)/(1 - x)^4.

Primes in this sequence: 199, 743, 15583, 105239, 435359, 620999, 770239, 853079, 1738423, 3511103, 7580119, 8737039, 10006063, ...

If a(n) is a positive prime then n is congruent to 0 or 4 (mod 6).

LINKS

Table of n, a(n) for n=0..40.

Ilya Gutkovskiy, Examples of the ordinary generating function for the values of cubic polynomialK

Eric Weisstein's World of Mathematics, Cubic Polynomial

Index entries for linear recurrences with constant coefficients, signature (4,-6, 4,-1).

FORMULA

G.f.: (-1 + 2*x + 17*x^2 + 6*x^3)/(1 - x)^4.

a(n) = A103532(n - 1) - A005408(n), n>0.

a(n) = 4*a(n -1) - 6*a(n - 2) + 4*a(n -  3) - a(n - 4).

Sum_(n>=0} 1/a(n) = -1.407823506818026589265...

MATHEMATICA

Table[4 n^3 - 3 n^2 - 2 n - 1, {n, 0, 40}]

LinearRecurrence[{4, -6, 4, -1}, {-1, -2, 15, 74}, 41]

CoefficientList[Series[(-1 + 2 x + 17 x^2 + 6 x^3) / (1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Feb 10 2016 *)

PROG

(MAGMA) [4*n^3-3*n^2-2*n-1: n in [0..40]]; Vincenzo Librandi, Feb 10 2016

(PARI) a(n)=4*n^3-3*n^2-2*n-1 \\ Charles R Greathouse IV, Jul 26 2016

CROSSREFS

Cf. A005408, A056578, A103532, A131464.

Sequence in context: A091135 A056037 A125903 * A178321 A007232 A308914

Adjacent sequences:  A268641 A268642 A268643 * A268645 A268646 A268647

KEYWORD

easy,sign

AUTHOR

Ilya Gutkovskiy, Feb 09 2016

STATUS

approved

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Last modified August 2 21:30 EDT 2021. Contains 346429 sequences. (Running on oeis4.)