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 A114901 Number of compositions of n such that each part is adjacent to an equal part. 46
 1, 0, 1, 1, 2, 1, 5, 3, 10, 10, 21, 22, 49, 51, 105, 126, 233, 292, 529, 678, 1181, 1585, 2654, 3654, 6016, 8416, 13606, 19395, 30840, 44517, 70087, 102070, 159304, 233941, 362429, 535520, 825358, 1225117, 1880220, 2801749, 4285086, 6404354, 9769782, 14634907 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..4000 N. J. A. Sloane, Transforms FORMULA INVERT(iMOEBIUS(iINVERT(A000012 shifted right 2 places))) EXAMPLE The 5 compositions of 6 are 3+3, 2+2+2, 2+2+1+1, 1+1+2+2, 1+1+1+1+1+1. From Gus Wiseman, Nov 25 2019: (Start) The a(2) = 1 through a(9) = 10 compositions: (11) (111) (22) (11111) (33) (11122) (44) (333) (1111) (222) (22111) (1133) (11133) (1122) (1111111) (2222) (33111) (2211) (3311) (111222) (111111) (11222) (222111) (22211) (1111122) (111122) (1112211) (112211) (1122111) (221111) (2211111) (11111111) (111111111) (End) MAPLE g:= proc(n, i) option remember; add(b(n-i*j, i), j=2..n/i) end: b:= proc(n, l) option remember; `if`(n=0, 1, add(`if`(i=l, 0, g(n, i)), i=1..n/2)) end: a:= n-> b(n, 0): seq(a(n), n=0..50); # Alois P. Heinz, Nov 29 2019 MATHEMATICA Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], Min@@Length/@Split[#]>1&]], {n, 0, 10}] (* Gus Wiseman, Nov 25 2019 *) g[n_, i_] := g[n, i] = Sum[b[n - i*j, i], {j, 2, n/i}] ; b[n_, l_] := b[n, l] = If[n==0, 1, Sum[If[i==l, 0, g[n, i]], {i, 1, n/2}]]; a[n_] := b[n, 0]; a /@ Range[0, 50] (* Jean-François Alcover, May 23 2021, after Alois P. Heinz *) CROSSREFS The case of partitions is A007690. Compositions with no adjacent parts equal are A003242. Compositions with all multiplicities > 1 are A240085. Compositions with minimum multiplicity 1 are A244164. Compositions with at least two adjacent parts equal are A261983. Cf. A178470, A238130, A274174, A329863. Sequence in context: A085261 A179218 A131119 * A355562 A194809 A113178 Adjacent sequences: A114898 A114899 A114900 * A114902 A114903 A114904 KEYWORD nonn AUTHOR Christian G. Bower, Jan 05 2006 STATUS approved

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Last modified April 22 13:50 EDT 2024. Contains 371903 sequences. (Running on oeis4.)