A135163 a(n) = 7^n - 5^n + 3^n - 2^n.

0, 3, 29, 237, 1841, 13893, 102689, 747477, 5380481, 38419653, 272767649, 1928673717, 13597673921, 95669893413, 672124323809, 4717058247957, 33080385660161, 231867703543173, 1624599287803169, 11379822860782197, 79696902351707201, 558069037383336933, 3907436894168837729

Offset

0,2

Comments

Constants are the prime numbers in decreasing order.

Links

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

Index entries for linear recurrences with constant coefficients, signature (17,-101,247,-210).

Formula

a(n) = 7^n - 5^n + 3^n - 2^n.

from Vincenzo Librandi, May 22 2014: (Start)

G.f.: 1/(1-7*x) - 1/(1-5*x) + 1/(1-3*x) - 1/(1-2*x).

a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4) for n>3. (End)

E.g.f.: exp(7*x) - exp(5*x) + exp(3*x) - exp(2*x). - G. C. Greubel, Sep 30 2016

Example

a(4) = 1841 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and 2401-625+81-16 = 1841.

Mathematica

CoefficientList[Series[1/(1 - 7 x) - 1/(1 - 5 x) + 1/(1 - 3 x) - 1/(1 - 2 x), {x, 0, 40}], x] (* Vincenzo Librandi, May 22 2014 *)
LinearRecurrence[{17, -101, 247, -210}, {0, 3, 29, 237}, 30] (* Harvey P. Dale, Sep 17 2016 *)

Prog

(Magma) [7^n-5^n+3^n-2^n: n in [0..50]]; // Vincenzo Librandi, Dec 14 2010
(Magma) I:=[0, 3, 29, 237]; [n le 4 select I[n] else 17*Self(n-1)-101*Self(n-2)+247*Self(n-3)-210*Self(n-4): n in [1..30]]; // Vincenzo Librandi, May 22 2014
(PARI) a(n) = 7^n - 5^n + 3^n - 2^n \\ Charles R Greathouse IV, Sep 30 2016

Crossrefs

Cf. A000079, A000244, A000351, A000420, A001047, A074527, A007689, A135158, A135159, A135160.

Sequence in context: A153825 A201490 A354402 * A074366 A037791 A037672

Adjacent sequences: A135160 A135161 A135162 * A135164 A135165 A135166

Keyword

nonn,easy

Author

Omar E. Pol, Nov 21 2007

Extensions

More terms from Vincenzo Librandi, Dec 14 2010

Status

approved