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A116150 a(n) = Sum_{j=1..n} (3^j + (-2)^j). 1
1, 14, 33, 130, 341, 1134, 3193, 10010, 29181, 89254, 264353, 799890, 2386021, 7185374, 21501513, 64613770, 193622861, 581305494, 1743042673, 5230875650, 15689131701, 47074385614, 141209175833, 423655489530, 1270910544541 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First primes are a(11)=264353 and a(17)=193622861. More primes?

Additional primes: a(71), a(91), a(431). - Harvey P. Dale, Jan 24 2013

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,5,-6).

FORMULA

a(n) = (9*3^n + 4*(-2)^n - 13)/6.

From G. C. Greubel, May 10 2019: (Start)

a(n) = 2*a(n-1) + 5*a(n-2) - 6*a(n-3).

G.f.: x*(1 + 12*x)/((1-x)*(1+2*x)*(1-3*x)).

E.g.f.: (4*exp(-2*x) - 13*exp(x) + 9*exp(3*x))/6.

MATHEMATICA

Accumulate[Table[3^i+(-2)^i, {i, 30}]] (* Harvey P. Dale, Jan 24 2013 *)

PROG

(PARI) {a(n) = (9*3^n + 4*(-2)^n - 13)/6}; \\ G. C. Greubel, May 10 2019

(MAGMA) [(9*3^n + 4*(-2)^n - 13)/6: n in [1..30]]; // G. C. Greubel, May 10 2019

(Sage) [(9*3^n + 4*(-2)^n - 13)/6 for n in (1..30)] # G. C. Greubel, May 10 2019

(GAP) List([1..30], n-> (9*3^n + 4*(-2)^n - 13)/6) # G. C. Greubel, May 10 2019

CROSSREFS

Sequence in context: A191866 A162279 A090090 * A019272 A018949 A007365

Adjacent sequences:  A116147 A116148 A116149 * A116151 A116152 A116153

KEYWORD

nonn

AUTHOR

Zak Seidov, Apr 14 2007

STATUS

approved

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Last modified September 25 00:02 EDT 2020. Contains 337333 sequences. (Running on oeis4.)