A230018 a(n) = (9*n^3 + 5*n)/2.

7, 41, 129, 298, 575, 987, 1561, 2324, 3303, 4525, 6017, 7806, 9919, 12383, 15225, 18472, 22151, 26289, 30913, 36050, 41727, 47971, 54809, 62268, 70375, 79157, 88641, 98854, 109823, 121575, 134137, 147536, 161799, 176953, 193025, 210042, 228031, 247019

Offset

1,1

Comments

7 and 41 are the only primes in the sequence.

Links

Table of n, a(n) for n=1..38.

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

Formula

a(n) = ceiling(1/f(n))/2, where f(n) = (n + 1/(3*n)) - (n^3 + n)^(1/3), n > 0.

Note that (n^3 + n)^(1/3) converges to n + 1/(3*n) as n -> infinity. Therefore f(n) is the residual.

From Colin Barker, Apr 01 2014: (Start)

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

G.f.: x*(7*x^2 + 13*x + 7) / (x-1)^4. (End)

Prog

(PARI) Vec(x*(7*x^2+13*x+7)/(x-1)^4 + O(x^100)) \\ Colin Barker, Apr 01 2014

Crossrefs

Sequence in context: A290204 A138629 A127923 * A165563 A034575 A237854

Adjacent sequences: A230015 A230016 A230017 * A230019 A230020 A230021

Keyword

nonn,easy

Author

Richard R. Forberg, Feb 22 2014

Extensions

More terms from Colin Barker, Apr 01 2014

Status

approved