This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A048159 Triangle giving a(n,k) = number of (n,k) labeled Greg trees (n >= 2, 0 <= k <= n-2). 9
 1, 3, 1, 16, 13, 3, 125, 171, 85, 15, 1296, 2551, 2005, 735, 105, 16807, 43653, 47586, 26950, 7875, 945, 262144, 850809, 1195383, 924238, 412650, 100485, 10395, 4782969, 18689527, 32291463, 31818045, 19235755, 7113645, 1486485, 135135 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS An (n,k) Greg tree can be described as a tree with n black nodes and k white nodes where only the black nodes are labeled and the white nodes are of degree at least 3. Row sums give A005263. LINKS C. Flight, How many stemmata?, Manuscripta, 34 (1990), 122-128. C. Flight, How many stemmata?, Manuscripta, 34 (1990), 122-128. (Annotated scanned copy) C. Flight, Letter to N. J. A. Sloane, Nov 1990 M. Josuat-Vergès, Derivatives of the tree function, arXiv preprint arXiv:1310.7531 [math.CO], 2013. Lucas Randazzo, Arboretum for a generalization of Ramanujan polynomials, arXiv:1905.02083 [math.CO], 2019. FORMULA a(n, 0) = n^(n-2), a(n, k) = (n+k-3)*a(n-1, k-1) + (2n+2k-3)*a(n-1, k) + (k+1)*a(n-1, k+1). EXAMPLE Triangle begins     1;     3,   1;    16,  13,   3;   125, 171,  85,  15;   ... MATHEMATICA a[n_, 0] := n^(n-2); a[n_ /; n >= 2, k_] /; 0 <= k <= n-2 := a[n, k] = (n+k-3)*a[n-1, k-1] + (2*n+2*k-3)*a[n-1, k] + (k+1)*a[n-1, k+1]; a[n_, k_] = 0; Table[a[n, k], {n, 2, 9}, {k, 0, n-2}] // Flatten (* Jean-François Alcover, Oct 03 2013 *) CROSSREFS Cf. A005264, A048160, A052300, A052301, A052302, A052303. Sequence in context: A038675 A264902 A156653 * A276640 A123527 A288265 Adjacent sequences:  A048156 A048157 A048158 * A048160 A048161 A048162 KEYWORD nonn,easy,tabl,nice AUTHOR EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Apr 07 2000 STATUS approved

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

Last modified November 19 16:37 EST 2019. Contains 329323 sequences. (Running on oeis4.)