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 A274199 Limiting reverse row of the array A274190. 22
 1, 1, 2, 3, 5, 8, 12, 19, 29, 44, 67, 101, 152, 228, 342, 511, 763, 1138, 1695, 2523, 3752, 5578, 8287, 12307, 18272, 27119, 40241, 59700, 88556, 131340, 194772, 288815, 428229, 634900, 941263, 1395397, 2068560, 3066372, 4545387, 6737633, 9987026, 14803303 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The triangular array (g(n,k)) at A274190 is defined as follows: g(n,k) = 1 for n >= 0; g(n,k) = 0 if k > n; g(n,k) = g(n-1,k-1) + g(n-1,2k) for n > 0, k > 1. From Gus Wiseman, Mar 12 2021: (Start) Also (apparently) the number of compositions of n where all adjacent parts (x, y), satisfy x < 2y. For example, the a(1) = 1 through a(6) = 12 compositions are: (1) (2) (3) (4) (5) (6) (11) (12) (13) (14) (15) (111) (22) (23) (24) (112) (32) (33) (1111) (113) (114) (122) (123) (1112) (132) (11111) (222) (1113) (1122) (11112) (111111) (End) LINKS Table of n, a(n) for n=0..41. Daniel Gabric and Jeffrey Shallit, Smallest and Largest Block Palindrome Factorizations, arXiv:2302.13147 [math.CO], 2023. EXAMPLE Row (g(14,k)): 1, 51, 73, 69, 55, 40, 28, 19, 12, 8, 5, 3, 2, 1, 1; the reversal is 1 1 2 3 5 8 12 19 28 ..., which agrees with A274199 up to 19. MATHEMATICA g[n_, 0] = g[n, 0] = 1; g[n_, k_] := g[n, k] = If[k > n, 0, g[n - 1, k - 1] + g[n - 1, 2 k]]; z = 300; u = Reverse[Table[g[z, k], {k, 0, z}]]; z = 301; v = Reverse[Table[g[z, k], {k, 0, z}]]; w = Join[{1}, Intersection[u, v]] (* A274199 *) Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], And@@Table[#[[i]]<2*#[[i-1]], {i, 2, Length[#]}]&]], {n, 15}] (* Gus Wiseman, Mar 12 2021 *) CROSSREFS Cf. A274190, A274200, A274201. Cf. A000929, A003242, A154402, A224957, A342094, A342095, A342096, A342097, A342098, A342191, A342330-A342342. Sequence in context: A355975 A327421 A124062 * A099823 A358335 A240523 Adjacent sequences: A274196 A274197 A274198 * A274200 A274201 A274202 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 13 2016 STATUS approved

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Last modified December 5 03:48 EST 2023. Contains 367567 sequences. (Running on oeis4.)