

A135166


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


1



2, 11, 69, 449, 2961, 19721, 132609, 899609, 6149121, 42287561, 292182849, 2025979769, 14084900481, 98108127401, 684321821889, 4778064771929, 33385475479041, 233393324431241, 1632227908017729, 11417967509964089, 79887630243516801, 559022690783231081, 3912205202997138369
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OFFSET

0,1


COMMENTS

Constants are the prime numbers in decreasing order.


LINKS

G. C. Greubel, 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)=2, a(1)=11, a(2)=69, a(3)=449, a(n) = 17*a(n1)  101*a(n2) + 247*a(n3)  210*a(n4).  Harvey P. Dale, Feb 01 2013
From G. C. Greubel, Sep 30 2016: (Start)
G.f.: (2  23*x + 84*x^2  107*x^3)/((1 2*x)*(1 3*x)*(1 5*x)*(1 7*x)).
E.g.f.: exp(7*x) + exp(5*x)  exp(3*x) + exp(2*x). (End)


EXAMPLE

a(4) = 2961 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and we can write 2401 + 625  81 + 16 = 2961.


MATHEMATICA

Table[7^n+5^n3^n+2^n, {n, 0, 30}] (* or *) LinearRecurrence[ {17, 101, 247, 210}, {2, 11, 69, 449}, 30] (* Harvey P. Dale, Feb 01 2013 *)


PROG

(MAGMA)[7^n+5^n3^n+2^n: n in [0..50]] // Vincenzo Librandi, Dec 14 2010
(PARI) a(n)=7^n+5^n3^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: A153393 A274736 A229230 * A118347 A250887 A047776
Adjacent sequences: A135163 A135164 A135165 * A135167 A135168 A135169


KEYWORD

easy,nonn


AUTHOR

Omar E. Pol, Nov 21 2007


EXTENSIONS

More terms from Vincenzo Librandi, Dec 14 2010


STATUS

approved



