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A135167 a(n) = 7^n + 5^n + 3^n - 2^n. Constants are the prime numbers in decreasing order. 2
2, 13, 79, 487, 3091, 20143, 133939, 903727, 6161731, 42325903, 292298899, 2026329967, 14085955171, 98111299663, 684331355059, 4778093404207, 33385561441411, 233393582449423, 1632228682334419, 11417969833438447, 79887637214988451, 559022711699743183, 3912205265750868979 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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.

From G. C. Greubel, Sep 30 2016: (Start)

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

G.f.: (2 - 21*x + 60*x^2 - 37*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)=3091 because 7^4=2401, 5^4=625, 3^4=81, 2^4=16 and we can write 2401+625+81-16=3091.

MATHEMATICA

Table[7^n + 5^n + 3^n - 2^n, {n, 0, 50}] (* or *) LinearRecurrence[{17, -101, 247, -210}, {2, 13, 79, 487}, 50] (* G. C. Greubel, Sep 30 2016 *)

PROG

(MAGMA)[7^n+5^n+3^n-2^n: n in [0..50]] // Vincenzo Librandi, Dec 15 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: A212390 A198849 A037555 * A271475 A037491 A037571

Adjacent sequences:  A135164 A135165 A135166 * A135168 A135169 A135170

KEYWORD

easy,nonn

AUTHOR

Omar E. Pol, Nov 21 2007

EXTENSIONS

More terms from Vincenzo Librandi, Dec 15 2010

STATUS

approved

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Last modified February 19 13:17 EST 2020. Contains 332044 sequences. (Running on oeis4.)