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

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A080952 2^(n-4)*(n+2)*(n+3)*(n+4)*(n+5)*(n+6)/15. 2
3, 21, 112, 504, 2016, 7392, 25344, 82368, 256256, 768768, 2236416, 6336512, 17547264, 47628288, 127008768, 333398016, 862912512, 2205220864, 5571084288, 13927710720, 34487664640, 84651540480, 206108098560, 498094571520 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Old definition was "Sequence associated with recurrence a(n)=2*a(n-1)+k(k+2)*a(n-2)". See the first comment in A080928.

The sixth column of A080928 (after 0) is 2*a(n).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index to sequences with linear recurrences with constant coefficients, signature (12,-60,160,-240,192,-64)

FORMULA

G.f.: (1-x)*(4*x^2-2*x+1)*(4*x^2-6*x+3)/(1-2x)^6.

a(n) = 12*a(n-1)-60*a(n-2)+160*a(n-3)-240*a(n-4)+192*a(n-5)-64*a(n-6), n>=6. [Harvey P. Dale, Jun 11 2011]

Let b(n) = A000292(n+1)+n+1+A000389(n+5) = (n+1)*(n^4+14*n^3+91*n^2+254*n+360)/120 = 3, 12, 34, 80, 166, 314,.. Then a(n) = 2^n*b(n) - 2^(n-1)*b(n-1). - R. J. Mathar, Jun 11 2011

MATHEMATICA

LinearRecurrence[{12, -60, 160, -240, 192, -64}, {3, 21, 112, 504, 2016, 7392}, 30] (* or *) CoefficientList[Series[(1-x) (3 - 12 x + 28 x^2 - 32 x^3 + 16 x^4)/ (1 - 2 x)^6, {x, 0, 30}], x] (* Harvey P. Dale, Jun 11 2011 *)

PROG

(MAGMA) I:=[3, 21, 112, 504, 2016, 7392]; [n le 6 select I[n] else 12*Self(n-1)-60*Self(n-2)+160*Self(n-3)-240*Self(n-4)+192*Self(n-5)-64*Self(n-6): n in [1..30]]; // Vincenzo Librandi, Aug 06 2013

CROSSREFS

Cf. A080928.

Sequence in context: A233582 A043012 A122120 * A183404 A121140 A005057

Adjacent sequences:  A080949 A080950 A080951 * A080953 A080954 A080955

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Feb 26 2003

EXTENSIONS

Replaced the previous definition with the closed form from Bruno Berselli, Aug 06 2013

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified November 21 11:17 EST 2014. Contains 249777 sequences.