login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A081187 5th binomial transform of (1,0,1,0,1,......), A059841. 5
1, 5, 26, 140, 776, 4400, 25376, 148160, 872576, 5169920, 30757376, 183495680, 1096779776, 6563901440, 39316299776, 235629363200, 1412702437376, 8471919656960, 50814338072576, 304817308958720, 1828628975845376 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A081187.

a(n) is also the number of words of length n over an alphabet of six letters, of which a chosen one appears an even number of times. See a comment in A007582, also for the crossrefs, for the 1- to 11- letter word cases. - Wolfdieter Lang, Jul 17 2017

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (10,-24).

FORMULA

a(n) = 10*a(n-1)-24*a(n-2) with n>1, a(0)=1, a(1)=5.

G.f.: (1-5*x)/((1-4*x)*(1-6*x)).

E.g.f. exp(5*x)*cosh(x).

a(n) = 4^n/2+6^n/2.

a(n) = Sum_{k=0..floor(n/2)} C(n, 2k)*5^(n-2k).

E.g.f.: exp(5*x)*cosh(x) = 1/2*E(0), where E(k)=1+(2^k)/(3^k-6*x*(9^k)/(6*x*(3^k)+(k+1)*(2^k)/E(k+1))); (continued fraction). - Sergei N. Gladkovskii, Nov 21 2011

MATHEMATICA

CoefficientList[Series[(1 - 5 x) / ((1 - 4 x) (1 - 6 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 07 2013 *)

PROG

(MAGMA) [4^n/2 + 6^n/2: n in [0..25]]; // Vincenzo Librandi, Aug 07 2013

CROSSREFS

Cf. A007582, A081189.

Sequence in context: A081569 A005573 A081911 * A182401 A104498 A045379

Adjacent sequences:  A081184 A081185 A081186 * A081188 A081189 A081190

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 11 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 14 07:19 EDT 2019. Contains 327995 sequences. (Running on oeis4.)