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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A077843 Expansion of (1-x)/(1-2*x-2*x^2-2*x^3). 1
1, 1, 4, 12, 34, 100, 292, 852, 2488, 7264, 21208, 61920, 180784, 527824, 1541056, 4499328, 13136416, 38353600, 111978688, 326937408, 954539392, 2786910976, 8136775552, 23756451840, 69360276736, 202507008256, 591247473664, 1726229517312, 5039967998464 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Invert transform of the sequence 1,3,5,5,5,5,... which has g.f. (1+2x+2x^2)/(1-x). - Paul Barry, Mar 01 2011

LINKS

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (2,2,2).

FORMULA

a(n) = sum(k=1..n, sum(i=k..n,(sum(j=0..k, binomial(j,-3*k+2*j+i)*2^(-2*k+j+i)* binomial(k,j)))*binomial(n+k-i-1,k-1))). - Vladimir Kruchinin, May 05 2011

EXAMPLE

Eigensequence of the triangle

  1,

  3, 1,

  5, 3, 1,

  5, 5, 3, 1,

  5, 5, 5, 3, 1,

  5, 5, 5, 5, 3, 1,

  5, 5, 5, 5, 5, 3, 1,

  5, 5, 5, 5, 5, 5, 3, 1,

  ...

- Paul Barry, Mar 01 2011

PROG

(Sage)

from sage.combinat.sloane_functions import recur_gen3

it = recur_gen3(0, 1, 1, 2, 2, 2)

[it.next() for i in range(35)] # Zerinvary Lajos, Jun 25 2008

(Maxima)

a(n):=sum(sum((sum(binomial(j, -3*k+2*j+i)*2^(-2*k+j+i)*binomial(k, j), j, 0, k))*binomial(n+k-i-1, k-1), i, k, n), k, 1, n); /* Vladimir Kruchinin, May 05 2011 */

(PARI) Vec((1-x)/(1-2*x-2*x^2-2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

CROSSREFS

Sequence in context: A005056 A014143 A077994 * A061703 A126948 A131593

Adjacent sequences:  A077840 A077841 A077842 * A077844 A077845 A077846

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 17 2002

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 18 18:56 EDT 2019. Contains 328197 sequences. (Running on oeis4.)