A220509 a(n) = n^3 + 3*n + 3^n.

1, 7, 23, 63, 157, 383, 963, 2551, 7097, 20439, 60079, 178511, 533205, 1596559, 4785755, 14352327, 43050865, 129145127, 387426375, 1162268383, 3486792461, 10460362527, 31381070323, 94143191063, 282429550377, 847288625143, 2541865845983, 7625597504751

Offset

0,2

Comments

This is to A220425 as 3 is to 2.

The subsequence of primes begins: 7, 23, 157, 383, 2551, see A220701 for the associated n.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-18,22,-13,3).

Formula

a(n) = n^3 + 3*n + 3^n = A000578(n) + A008585(n) + A000244(n).

G.f.: (1 - 8*x^2 + 6*x^3 - 11*x^4)/((1-x)^4*(1-3*x)). - Vincenzo Librandi, Dec 18 2012

Example

a(1) = 1^3 + 3*1 + 3^1 = 7.
a(2) = 2^3 + 3*2 + 3^2 = 23.

Mathematica

Table[n^3 + 3*n + 3^n, {n, 0, 30}] (* T. D. Noe, Dec 17 2012 *)
CoefficientList[Series[(1 - 8*x^2 + 6*x^3 - 11*x^4)/((1-x)^4*(1-3x)), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 18 2012 *)
LinearRecurrence[{7, -18, 22, -13, 3}, {1, 7, 23, 63, 157}, 30] (* Harvey P. Dale, Dec 17 2025 *)

Prog

(Maxima) A220509(n):=n^3+3*n+3^n$ makelist(A220509(n), n, 0, 20); /* Martin Ettl, Dec 17 2012 */
(Magma) [n^3 + 3*n + 3^n: n in [0..30]]; // Vincenzo Librandi, Dec 18 2012

Crossrefs

Cf. A000244, A000578, A008585, A220425, A220701.

Sequence in context: A077037 A201110 A333187 * A003261 A306971 A343519

Adjacent sequences: A220506 A220507 A220508 * A220510 A220511 A220512

Keyword

nonn,easy

Author

Jonathan Vos Post, Dec 15 2012

Status

approved