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Triangle T(n,k) (n >= 2, 1 <= k <= n-1) read by rows: row n gives epispectrum of a path P_n (see reference for precise definition).
2

%I #12 Nov 21 2018 02:37:35

%S 1,1,1,1,2,1,1,2,4,1,1,2,6,6,1,1,2,7,11,10,1,1,2,8,14,24,14,1,1,2,9,

%T 16,35,42,22,1,1,2,10,18,45,68,81,30,1,1,2,11,20,55,89,149,138,46,1,1,

%U 2,12,22,66,110,216,282,250,62,1,1,2,13,24,78,132,285,422,577,419

%N Triangle T(n,k) (n >= 2, 1 <= k <= n-1) read by rows: row n gives epispectrum of a path P_n (see reference for precise definition).

%H Toufik Mansour, Armend Sh. Shabani, <a href="https://doi.org/10.3906/mat-1803-113">Bargraphs in bargraphs</a>, Turkish Journal of Mathematics (2018) Vol. 42, Issue 5, 2763-2773.

%H M. A. Michels and U. Knauer, <a href="http://dx.doi.org/10.1016/j.disc.2008.11.022">The congruence classes of paths and cycles</a>, Discr. Math., 309 (2009), 5352-5359.

%e Triangle begins:

%e 1;

%e 1, 1;

%e 1, 2, 1;

%e 1, 2, 4, 1;

%e 1, 2, 6, 6, 1;

%e 1, 2, 7, 11, 10, 1;

%e 1, 2, 8, 14, 24, 14, 1;

%e 1, 2, 9, 16, 35, 42, 22, 1;

%e 1, 2, 10, 18, 45, 68, 81, 30, 1;

%e 1, 2, 11, 20, 55, 89, 149, 138, 46, 1;

%e 1, 2, 12, 22, 66, 110, 216, 282, 250, 62, 1;

%e 1, 2, 13, 24, 78, 132, 285, 422, 577, 419, 94, 1;

%e 1, 2, 14, 26, 91, 156, 364, 568, 945, 1070, 732, 126, 1;

%Y Cf. A152086, A102699.

%K nonn,tabl

%O 2,5

%A _N. J. A. Sloane_, Sep 20 2009