The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A293172 Triangle read by rows: T(n,k) = number of colored weighted Motzkin paths ending at (n,k). 1
 1, 6, 1, 40, 10, 1, 280, 84, 14, 1, 2016, 672, 144, 18, 1, 14784, 5280, 1320, 220, 22, 1, 109824, 41184, 11440, 2288, 312, 26, 1, 823680, 320320, 96096, 21840, 3640, 420, 30, 1, 6223360, 2489344, 792064, 198016, 38080, 5440, 544, 34, 1, 47297536, 19348992, 6449664, 1736448, 372096, 62016, 7752 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..51. Sheng-Liang Yang, Yan-Ni Dong, and Tian-Xiao He, Some matrix identities on colored Motzkin paths, Discrete Mathematics 340.12 (2017): 3081-3091. See p. 3088. EXAMPLE Triangle begins: 1, 6,1, 40,10,1, 280,84,14,1, 2016,672,144,18,1, 14784,5280,1320,220,22,1, ... MAPLE A293172 := proc(n, k) option remember; local b, d, r, c, e; b := 4; d:= 2; r := 2 ; c := r^2 ; e := d ; if k < 0 or k > n then 0; elif k = n then 1; elif k = 0 then (b+e)*procname(n-1, 0)+c*procname(n-1, 1) ; else procname(n-1, k-1)+b*procname(n-1, k)+c*procname(n-1, k+1) ; end if; end proc: seq(seq( A293172(n, k), k=0..n), n=0..15) ; # R. J. Mathar, Oct 27 2017 MATHEMATICA T[n_, k_] := T[n, k] = Module[{b = 4, d = 2, r = 2, c, e}, c = r^2; e = d; If[k < 0 || k > n, 0, If[k == n, 1, If[k == 0, (b + e) T[n - 1, 0] + c T[n - 1, 1], T[n - 1, k - 1] + b T[n - 1, k] + c T[n - 1, k + 1]]]]]; Table[T[n, k], {n, 0, 15}, {k, 0, n}] // Flatten (* Jean-François Alcover, Apr 07 2020, from Maple *) CROSSREFS First column is A069720. Sequence in context: A089504 A145927 A113365 * A145356 A145357 A035529 Adjacent sequences: A293169 A293170 A293171 * A293173 A293174 A293175 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Oct 19 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 24 16:36 EDT 2024. Contains 373680 sequences. (Running on oeis4.)