login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A238422 Number of compositions of n where no consecutive parts differ by 1. 1
1, 1, 2, 2, 5, 7, 15, 23, 43, 70, 128, 214, 383, 651, 1149, 1971, 3457, 5961, 10412, 18011, 31384, 54384, 94639, 164163, 285454, 495452, 861129, 1495126, 2597970, 4511573, 7838280, 13613289, 23649355, 41076088, 71354998, 123939602, 215294730, 373962643, 649597906, 1128352145 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) ~ c * d^n, where c = 0.501153706040308227351395770679776260606990346633815... and d = 1.737029107886986816124470304294547513896522086125645631179... - Vaclav Kotesovec, Feb 26 2014

EXAMPLE

The a(6) = 15 such compositions are:

01:  [ 1 1 1 1 1 1 ]

02:  [ 1 1 1 3 ]

03:  [ 1 1 3 1 ]

04:  [ 1 1 4 ]

05:  [ 1 3 1 1 ]

06:  [ 1 4 1 ]

07:  [ 1 5 ]

08:  [ 2 2 2 ]

09:  [ 2 4 ]

10:  [ 3 1 1 1 ]

11:  [ 3 3 ]

12:  [ 4 1 1 ]

13:  [ 4 2 ]

14:  [ 5 1 ]

15:  [ 6 ]

MAPLE

# b(n, i): number of compositions of n where the leftmost part j

#          and i do not have distance 1

b:= proc(n, i) option remember; `if`(n=0, 1,

      add(`if`(abs(i-j)=1, 0, b(n-j, j)), j=1..n))

    end:

a:= n-> b(n, -1):

seq(a(n), n=0..50);

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[If[Abs[i - j] == 1, 0, b[n - j, j]], {j, 1, n}]]; a[n_] := b[n, -1]; Table[a[n], {n, 0, 50}] (* Jean-Fran├žois Alcover, Nov 06 2014, after Maple *)

CROSSREFS

Cf. A116931 (partitions where no consecutive parts differ by 1).

Sequence in context: A255063 A195964 A047083 * A327019 A035085 A208238

Adjacent sequences:  A238419 A238420 A238421 * A238423 A238424 A238425

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Feb 26 2014

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 January 23 22:36 EST 2020. Contains 331177 sequences. (Running on oeis4.)