|
Search: id:A007068
|
|
|
| A007068 |
|
a(n) = a(n-1) + (3+(-1)^n)*a(n-2)/2.
(Formerly M2360)
|
|
+0
5
|
|
| 1, 3, 4, 10, 14, 34, 48, 116, 164, 396, 560, 1352, 1912, 4616, 6528, 15760, 22288, 53808, 76096, 183712, 259808, 627232, 887040, 2141504, 3028544, 7311552, 10340096, 24963200, 35303296, 85229696, 120532992, 290992384, 411525376
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
First row of spectral array W(sqrt 2).
Row sums of the square of the matrix with general term binomial(floor(n/2),n-k). - Paul Barry (pbarry(AT)wit.ie), Feb 14 2005
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A. Fraenkel and C. Kimberling, "Generalized Wythoff arrays, shuffles and interspersions," Discrete Mathematics 126 (1994) 137-149.
|
|
FORMULA
|
a(2n+1)=a(2n)+a(2n-1); a(2n)=a(2n-1)+2*a(2n-2); same recurrence (mod parity) as A001882) - Len Smiley (smiley(AT)math.uaa.alaska.edu), Feb 05 2001.
a(n)=sum{k=0..n, sum{j=0..n, C(floor(n/2), n-j)*C(floor(j/2), j-k)}} - Paul Barry (pbarry(AT)wit.ie), Feb 14 2005
a(n)=4*a(n-2)-2*a(n-4). G.f.: -x*(1+x)*(2*x^2-2*x-1)/(1-4*x^2+2*x^4). a(2n+1)=A007070(n). a(2n)=A007052(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 17 2009]
|
|
CROSSREFS
|
Cf. A062112.
Sequence in context: A134512 A106523 A121720 this_sequence A056515 A056516 A056517
Adjacent sequences: A007065 A007066 A007067 this_sequence A007069 A007070 A007071
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein (mira(AT)math.berkeley.edu)
|
|
EXTENSIONS
|
Better description and more terms from Olivier Gerard (olivier.gerard(AT)gmail.com), Jun 05 2001
|
|
|
Search completed in 0.002 seconds
|
