login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A243456 a(n+6) = 6*a(n+4) - 12*a(n+2) + 8*a(n), a(0)..a(5) = 8,0,9,0,8,0. 3
8, 0, 9, 0, 8, 0, 4, 0, 0, 0, 16, 0, 128, 0, 576, 0, 2048, 0, 6400, 0, 18432, 0, 50176, 0, 131072, 0, 331776, 0, 819200, 0, 1982464, 0, 4718592, 0, 11075584, 0, 25690112, 0, 58982400, 0, 134217728, 0, 303038464, 0, 679477248, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The infinite sum of the reciprocals of the even terms a(2*k) for k>=5 yields (1/96)*(Pi^2 - 6*log^2(2)). That is, sum(k>=1, 1/(k^2*2^k) = dilog(1/2) = (Pi^2 - 6*(log(2))^2)/12. See the Jolley reference, pp. 66-69, (360) (c), and Abramowitz-Stegun, p. 1004, 27.7.3 for x=1/2. For the decimal expansion of dilog(1/2) see A076788.

REFERENCES

L. B. W. Jolley, Summation of Series, Dover (1961).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

G. Myerson and A. J. van der Poorten, Some problems concerning recurrence sequences, Amer. Math. Monthly 102 (1995), no. 8, 698-705.

Index entries for linear recurrences with constant coefficients, signature (0,6,0,-12,0,8).

FORMULA

a(n) = 0, if n is odd, a(n) = (n - 8)^2*2^((n-6)/2), if n is even.

a(n) = 2^(n/2 - 4)*(1 + (-1)^n)*(n - 8)^2.

a(n+2) = (2*(n-6)^2*a(n))/(n-8)^2, n>=0, with a(0) = 8, a(1) = 0 and a(10) = 0/0 := 16.

G.f.: (8 - 39*x^2 + 50*x^4)/(1-2*x^2)^3.

MAPLE

A243456:=n->2^(n/2 - 4)*(1 + (-1)^n)*(n - 8)^2; seq(A243456(n), n=0..50); # Wesley Ivan Hurt, Jun 08 2014

MATHEMATICA

Table[2^(n/2 - 4)*(1 + (-1)^n)*(n - 8)^2, {n, 0, 50}] (* Wesley Ivan Hurt, Jun 08 2014 *)

CoefficientList[Series[(8 - 39 x^2 + 50 x^4)/(1 - 2 x^2)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 16 2014 *)

LinearRecurrence[{0, 6, 0, -12, 0, 8}, {8, 0, 9, 0, 8, 0}, 50] (* Harvey P. Dale, Mar 02 2016 *)

CROSSREFS

Cf. A076788.

Sequence in context: A005076 A296182 A019863 * A246772 A198820 A138285

Adjacent sequences:  A243453 A243454 A243455 * A243457 A243458 A243459

KEYWORD

nonn

AUTHOR

Alexander R. Povolotsky, Jun 05 2014

EXTENSIONS

Comment on the sum reformulated and Jolley and Abramowitz-Stegun reference added. G.f. corrected for offset 0. In the recurrence a(10) defined. - Wolfdieter Lang, Jun 16 2014

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 17 11:43 EDT 2021. Contains 348048 sequences. (Running on oeis4.)