Number of compositions of n such that one maximal run is the longest.

Terms

a(0) =1a(1) =1a(2) =2a(3) =2a(4) =5a(5) =10a(6) =16a(7) =39a(8) =81a(9) =156a(10) =323a(11) =672a(12) =1334a(13) =2704a(14) =5471a(15) =10956a(16) =21985a(17) =44143a(18) =88366a(19) =176961a(20) =354236a(21) =708688a(22) =1417905a(23) =2836907a(24) =5675282a(25) =11354249a(26) =22717973a(27) =45457421a(28) =90965933a(29) =182051395