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 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-François 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

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