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A135162 a(n) = 7^n - 5^n - 3^n + 2^n. Constants are the prime numbers in decreasing order. 1
0, 1, 19, 199, 1711, 13471, 101359, 743359, 5367871, 38381311, 272651599, 1928323519, 13596619231, 95666721151, 672114790639, 4717029615679, 33080299697791, 231867445524991, 1624598513486479, 11379820537307839, 79696895380235551, 558069016466824831, 3907436831415107119 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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.

a(0)=0, a(1)=1, a(2)=19, a(3)=199, a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4). - Harvey P. Dale, Dec 13 2013

G.f.: 1/(1-7*x) - 1/(1-5*x) - 1/(1-3*x) + 1/(1-2 x). - Vincenzo Librandi, May 22 2014

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

EXAMPLE

a(4) = 1711 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and 2401-625-81+16 = 1711.

MATHEMATICA

Table[7^n-5^n-3^n+2^n, {n, 0, 30}] (* or *) LinearRecurrence[ {17, -101, 247, -210}, {0, 1, 19, 199}, 30] (* Harvey P. Dale, Dec 13 2013 *)

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 *)

PROG

(MAGMA) [7^n-5^n-3^n+2^n: n in [0..50]]; // Vincenzo Librandi, Dec 14 2010

(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: A164890 A066007 A147830 * A185687 A067272 A065582

Adjacent sequences:  A135159 A135160 A135161 * A135163 A135164 A135165

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Nov 21 2007

EXTENSIONS

More terms from Vincenzo Librandi, Dec 14 2010

STATUS

approved

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Last modified April 22 10:24 EDT 2019. Contains 322330 sequences. (Running on oeis4.)