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A034513 1^n + 3^n + 9^n. 88
3, 13, 91, 757, 6643, 59293, 532171, 4785157, 43053283, 387440173, 3486843451, 31381236757, 282430067923, 2541867422653, 22876797237931, 205891146443557, 1853020231898563, 16677181828806733, 150094635684419611 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Also the sum of n-th powers of the divisors of 9.

LINKS

T. D. Noe, Table of n, a(n) for n=0..200

Index entries for linear recurrences with constant coefficients, signature (13,-39,27).

FORMULA

G.f.: 1/(1-x)+1/(1-3*x)+1/(1-9*x). E.g.f.: e^x+e^(3*x)+e^(9*x). [From Mohammad K. Azarian, Dec 26 2008]

a(0)=3, a(1)=13, a(2)=91, a(n)=13*a(n-1)-39*a(n-2)+27*a(n-3) [From Harvey P. Dale, Apr 13 2012]

MATHEMATICA

Table[1^n + 3^n + 9^n, {n, 0, 20}]

LinearRecurrence[{13, -39, 27}, {3, 13, 91}, 20] (* Harvey P. Dale, Apr 13 2012 *)

PROG

(Sage) [sigma(9, n)for n in xrange(0, 19)] # [From Zerinvary Lajos, Jun 04 2009]

(PARI) a(n)=1+3^n+9^n \\ Charles R Greathouse IV, Jun 10 2011

CROSSREFS

Cf. A001550, A001576, A001579, A074501 - A074580.

Sequence in context: A114477 A116434 A174290 * A098462 A257661 A292501

Adjacent sequences:  A034510 A034511 A034512 * A034514 A034515 A034516

KEYWORD

easy,nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 18 05:08 EST 2017. Contains 294853 sequences.