The On-Line Encyclopedia of Integer Sequences (OEIS)

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Expansion of (1+x-x^2)/(1-2x-2x^2+x^4).
(history; published version)

#6 by Charles R Greathouse IV at Sat Jun 13 00:51:51 EDT 2015

LINKS

<a href="/index/Rec#order_04">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (2,2,0,-1).

Discussion

Sat Jun 13

00:51

OEIS Server: https://oeis.org/edit/global/2439

#5 by R. J. Mathar at Fri Feb 20 17:41:31 EST 2015

STATUS

editing

approved

#4 by R. J. Mathar at Fri Feb 20 17:41:27 EST 2015

LINKS

<a href="/index/Rec#order_04">Index to sequences with linear recurrences with constant coefficients</a>, signature (2,2,0,-1).

STATUS

approved

editing

#3 by Russ Cox at Fri Mar 30 18:59:08 EDT 2012

AUTHOR

_Paul Barry (pbarry(AT)wit.ie), _, Jun 22 2005

Discussion

Fri Mar 30

18:59

OEIS Server: https://oeis.org/edit/global/287

#2 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

FORMULA

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

KEYWORD

easy,nonn,new

#1 by N. J. A. Sloane at Tue Jul 19 03:00:00 EDT 2005

NAME

Expansion of (1+x-x^2)/(1-2x-2x^2+x^4).

DATA

1, 3, 7, 20, 53, 143, 385, 1036, 2789, 7507, 20207, 54392, 146409, 394095, 1060801, 2855400, 7685993, 20688691, 55688567, 149899116, 403489373, 1086088287, 2923466753, 7869210964, 21181866061, 57016065763, 153472396895

OFFSET

0,2

COMMENTS

Transform of 2^n under matrix A108756.

FORMULA

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

KEYWORD

easy,nonn

AUTHOR

Paul Barry (pbarry(AT)wit.ie), Jun 22 2005

STATUS

approved