Original entry on oeis.org
1, 2, 4, 9, 23, 63, 176, 491, 1362, 3762, 10369, 28559, 78653, 216638, 596761, 1643966, 4528932, 12476737, 34372059, 94691059, 260862508, 718644363, 1979777046, 5454042866, 15025219777, 41392641187, 114031662049, 314143279634, 865426307713, 2384143611738, 6568023995156
Offset: 0
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LinearRecurrence[{5,-8,5},{1,1,2,4},31]
A372879
Irregular triangle read by rows: T(n,k) is the number of flattened Catalan words of length n with exactly k short peak, with k >= 0.
Original entry on oeis.org
1, 2, 4, 1, 9, 5, 22, 18, 1, 56, 58, 8, 145, 178, 41, 1, 378, 532, 173, 11, 988, 1563, 656, 73, 1, 2585, 4535, 2327, 381, 14, 6766, 13030, 7888, 1726, 114, 1, 17712, 37140, 25872, 7124, 709, 17, 46369, 105156, 82758, 27534, 3739, 164, 1, 121394, 296040, 259542, 101350, 17632, 1184, 20
Offset: 1
The irregular triangle begins:
1;
2;
4, 1;
9, 5;
22, 18, 1;
56, 58, 8;
145, 178, 41, 1;
378, 532, 173, 11;
988, 1563, 656, 73, 1;
...
T(6,2) = 8 since there are 8 flattened Catalan words of length 6 with 2 short peaks: 001010, 010100, 010101, 010010, 010120, 010121, 012010, and 012121.
- Jean-Luc Baril, Pamela E. Harris, and José L. Ramírez, Flattened Catalan Words, arXiv:2405.05357 [math.CO], 2024. See pp. 19-20.
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T[n_,k_]:=SeriesCoefficient[x(1-2x)/((1-x)(1-3x+x^2(1-y))),{x,0,n},{y,0,k}]; Table[T[n,k],{n,14},{k,0,Floor[(n-1)/2]}]//Flatten
A372884
a(n) is the sum of all symmetric peaks in the set of flattened Catalan words of length n.
Original entry on oeis.org
1, 5, 19, 67, 230, 778, 2602, 8618, 28303, 92275, 298949, 963253, 3089020, 9864896, 31388260, 99545572, 314779181, 992765041, 3123577735, 9806581175, 30727287586, 96104495110, 300081382574, 935547839662, 2912554595035, 9055397013503, 28119390725977, 87217771234633
Offset: 3
- Jean-Luc Baril, Pamela E. Harris, and José L. Ramírez, Flattened Catalan Words, arXiv:2405.05357 [math.CO], 2024. See p. 22.
- Index entries for linear recurrences with constant coefficients, signature (9,-30,46,-33,9).
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LinearRecurrence[{9,-30,46,-33,9},{1,5,19,67,230},28]
Showing 1-3 of 3 results.