|
| |
|
|
A075535
|
|
a(1)=1, a(n) = sum( k=1,n-1, min(a(k),a(n-k)) ).
|
|
2
| |
|
|
1, 1, 2, 3, 4, 6, 8, 11, 14, 18, 22, 28, 34, 42, 50, 61, 72, 86, 100, 118, 136, 158, 180, 208, 236, 270, 304, 346, 388, 438, 488, 549, 610, 682, 754, 840, 926, 1026, 1126, 1244, 1362, 1498, 1634, 1792, 1950, 2130, 2310, 2518, 2726, 2962, 3198, 3468, 3738, 4042
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| Sequence gives (1/2) of the number of unique path partitions of the integer 2n; see the function w(n) as defined in the paper by Bessenrodt, Olsson, and Sellers.
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
Christine Bessenrodt, Jorn B. Olsson, and James A. Sellers, Unique path partitions: Characterization and Congruences, arXiv preprint
|
|
|
FORMULA
| a(1)=a(2)=1; a(2n)=a(2n-1)+a(n); a(2n+1)=a(2n)+a(n); n>=3 a(n)=a(n-1)+a(floor(n/2))
Let T(x) be the g.f. 1 + x + 2*x^2 + 3*x^3+... (i.e. with offset 0), then T(x) = 1 + x * (1+x)/(1-x) * T(x^2). [Joerg Arndt, May 11 2010]
|
|
|
MATHEMATICA
| Fold[Append[#1, Total[Take[Flatten[Transpose[{#1, #1}]], #2]]] &, {1}, Range[53]] (* Gyorgy Birkas, Apr 18 2011 *)
a[1] = 1; a[2] = 1; a[n_] := a[n] = a[n - 1] + a[Floor[n/2]]; Array[a, 100] (* T. D. Noe, Apr 18 2011 *)
|
|
|
PROG
| (PARI) a(n)=if(n<3, 1, a(n-1)+a(floor(n/2)))
|
|
|
CROSSREFS
| Cf. A033485.
Sequence in context: A071764 A059291 A177339 * A134953 A175870 A114829
Adjacent sequences: A075532 A075533 A075534 * A075536 A075537 A075538
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 11 2003
|
| |
|
|
