|
| |
|
|
A029907
|
|
a(n+1) = a(n) + a(n-1) + Fibonacci(n).
|
|
16
| |
|
|
0, 1, 2, 4, 8, 15, 28, 51, 92, 164, 290, 509, 888, 1541, 2662, 4580, 7852, 13419, 22868, 38871, 65920, 111556, 188422, 317689, 534768, 898825, 1508618, 2528836, 4233872, 7080519, 11828620, 19741179, 32916068, 54835556, 91276202
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Number of matchings of the fan graph on n vertices, n>0 (a fan is the join of the path graph with one extra vertex).
a(n+1) gives row sums of A054450. - Paul Barry (pbarry(AT)wit.ie), Oct 23 2004
Number of parts in all compositions of n into odd parts. Example: a(5)=15 because the compositions 5, 311, 131, 113, and 11111 have a total of 1+3+3+3+5=15 parts.
|
|
|
LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (2,1,-2,-1)
|
|
|
FORMULA
| G.f.: x*(1-x^2)/(1-x-x^2)^2. a(n)= ((n+4)*F(n)+2*n*F(n-1))/5, F(n)=A000045(n) (Fibonacci).
a(n+1)=sum{k=0..n, sum{j=0..floor(k/2), binomial(n-j, j)}}. - Paul Barry (pbarry(AT)wit.ie), Oct 23 2004
a(n) = A010049(n+1) +A152163(n+1). - R. J. Mathar, Dec 10 2011
|
|
|
EXAMPLE
| a(4)=8 because matchings of fan graph with edges {OA,OB,OC,AB,AC} are {},{OA},{OB},{OC},{AB},{AC},{OA,BC},{OC,AB}.
|
|
|
MAPLE
| with(combinat); A029907 := proc(n) options remember; if n <= 1 then n else procname(n-1)+procname(n-2)+fibonacci(n-1); fi; end;
|
|
|
PROG
| (PARI) alias(F, fibonacci); a(n)=((n+4)*F(n)+2*n*F(n-1))/5
|
|
|
CROSSREFS
| Sequence in context: A006808 A006727 A182725 * A005682 A114833 A065617
Adjacent sequences: A029904 A029905 A029906 * A029908 A029909 A029910
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Additional formula from Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 02 2000
Additional comments from Michael Somos, Jul 23, 2002
|
| |
|
|
