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A081343 (10^n+4^n)/2. 4
1, 7, 58, 532, 5128, 50512, 502048, 5008192, 50032768, 500131072, 5000524288, 50002097152, 500008388608, 5000033554432, 50000134217728, 500000536870912, 5000002147483648, 50000008589934592, 500000034359738368 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A025551. 7th binomial transform of (1,0,9,0,81,0,729,0,...).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (14,-40).

FORMULA

a(n) = 14*a(n-1) -40*a(n-2), a(0)=1, a(1)=7.

G.f.: (1-7*x)/((1-4*x)*(1-10*x)).

E.g.f.: exp(7*x) * cosh(3*x).

a(n) = ((7+sqrt9)^n+(7-sqrt9)^n)/2. [Al Hakanson (hawkuu(AT)gmail.com), Dec 08 2008]

MATHEMATICA

CoefficientList[Series[(1 - 7 x) / ((1 - 4 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 08 2013 *)

PROG

(MAGMA) [(10^n+4^n)/2: n in [0..25]]; // Vincenzo Librandi, Aug 08 2013

(PARI) a(n)=(10^n+4^n)/2 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A081342.

Sequence in context: A006193 A139397 A194724 * A163048 A192940 A126130

Adjacent sequences:  A081340 A081341 A081342 * A081344 A081345 A081346

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 18 2003

STATUS

approved

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Last modified February 25 03:06 EST 2018. Contains 299630 sequences. (Running on oeis4.)