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 A325689 Number of length-3 compositions of n such that no part is the sum of the other two. 6
 0, 0, 0, 1, 0, 6, 4, 15, 12, 28, 24, 45, 40, 66, 60, 91, 84, 120, 112, 153, 144, 190, 180, 231, 220, 276, 264, 325, 312, 378, 364, 435, 420, 496, 480, 561, 544, 630, 612, 703, 684, 780, 760, 861, 840, 946, 924, 1035, 1012, 1128, 1104, 1225, 1200, 1326, 1300, 1431 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS A composition of n is a finite sequence of positive integers summing to n. Confirmed recurrence relation from Colin Barker for n <= 5000. - Fausto A. C. Cariboni, Feb 15 2022 LINKS Fausto A. C. Cariboni, Table of n, a(n) for n = 0..5000 FORMULA Conjectures from Colin Barker, May 16 2019: (Start) G.f.: x^3*(1 - x + 4*x^2) / ((1 - x)^3*(1 + x)^2) for n>5. a(n) = -(5 + 3*(-1)^n - 2*n) * (n-2) / 4 for n>0. a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5). (End) EXAMPLE The a(3) = 1 through a(8) = 12 compositions (empty columns not shown): (111) (113) (114) (115) (116) (122) (141) (124) (125) (131) (222) (133) (152) (212) (411) (142) (161) (221) (151) (215) (311) (214) (233) (223) (251) (232) (323) (241) (332) (313) (512) (322) (521) (331) (611) (412) (421) (511) MATHEMATICA Table[Length[Select[Join@@Permutations/@IntegerPartitions[n, {3}], And@@Table[#[[i]]!=Total[Delete[#, i]], {i, 3}]&]], {n, 0, 30}] CROSSREFS Cf. A000079, A001399, A005044, A008642, A069905, A124278, A266223. Cf. A325676, A325688, A325690, A325691, A325694. Sequence in context: A096038 A064462 A248266 * A199890 A198459 A083581 Adjacent sequences: A325686 A325687 A325688 * A325690 A325691 A325692 KEYWORD nonn AUTHOR Gus Wiseman, May 15 2019 STATUS approved

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Last modified September 22 10:28 EDT 2023. Contains 365520 sequences. (Running on oeis4.)