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A086760

a(n) = 8*n^2 + 88*n + 43.

43, 139, 251, 379, 523, 683, 859, 1051, 1259, 1483, 1723, 1979, 2251, 2539, 2843, 3163, 3499, 3851, 4219, 4603, 5003, 5419, 5851, 6299, 6763, 7243, 7739, 8251, 8779, 9323, 9883, 10459, 11051, 11659, 12283, 12923, 13579, 14251, 14939, 15643, 16363, 17099

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OFFSET

0,1

COMMENTS

The start of the sequence is rich in primes.

The first nonprime (for n >= 0) occurs at n=27. Also 449 of the first 1000 terms are nonprimes and half of the first 1516 terms are nonprimes. - Harvey P. Dale, Sep 29 2016

LINKS

Table of n, a(n) for n=0..41.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

From Elmo R. Oliveira, Nov 11 2025: (Start)

G.f.: (43 + 10*x - 37*x^2)/(1-x)^3.

E.g.f.: (43 + 96*x + 8*x^2)*exp(x).

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

MATHEMATICA

Table[8n^2+88n+43, {n, 0, 100}] (* Harvey P. Dale, Sep 29 2016 *)

PROG

(PARI) a(n)=8*n^2+88*n+43 \\ Charles R Greathouse IV, Jun 17 2017