login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A099462 Expansion of x/(1 - 4*x^2 - 4*x^3). 2
0, 1, 0, 4, 4, 16, 32, 80, 192, 448, 1088, 2560, 6144, 14592, 34816, 82944, 197632, 471040, 1122304, 2674688, 6373376, 15187968, 36192256, 86245376, 205520896, 489750528, 1167065088, 2781085696, 6627262464, 15792603136, 37633392640 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Binomial transform is A099463.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,4,4).

FORMULA

a(n) = 4*a(n-2) + 4*a(n-3).

a(n) = Sum_{k=0..floor((n-1)/2)} binomial(k, n-2*k-1)*4^k.

a(n+1) = Sum_{k=0..floor(n/2)} C((n-k)/2, k)*(1+(-1)^(n-k))*2^(n-k). - Paul Barry, Sep 09 2005

MATHEMATICA

LinearRecurrence[{0, 4, 4}, {0, 1, 0}, 40] (* G. C. Greubel, Nov 18 2021 *)

PROG

(Magma) [n le 3 select (1+(-1)^n)/2 else 4*(Self(n-2) +Self(n-3)): n in [1..41]]; // G. C. Greubel, Nov 18 2021

(Sage)

def a(n): return sum( 4^k*binomial(k, n-2*k-1) for k in (0..(n-1)//2) )

[a(n) for n in (0..40)] # G. C. Greubel, Nov 18 2021

CROSSREFS

Cf. A099463.

Sequence in context: A322039 A158101 A038234 * A218051 A092266 A257606

Adjacent sequences: A099459 A099460 A099461 * A099463 A099464 A099465

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 16 2004

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 14:20 EST 2022. Contains 358656 sequences. (Running on oeis4.)