A107984 Triangle read by rows: T(n,k) = (k+1)*(n+2)*(2n-k+3)*(n-k+1)/6 for 0 <= k <= n.
1, 5, 4, 14, 16, 10, 30, 40, 35, 20, 55, 80, 81, 64, 35, 91, 140, 154, 140, 105, 56, 140, 224, 260, 256, 220, 160, 84, 204, 336, 405, 420, 390, 324, 231, 120, 285, 480, 595, 640, 625, 560, 455, 320, 165, 385, 660, 836, 924, 935, 880, 770, 616, 429, 220, 506, 880
Offset: 0
Examples
Triangle begins: 1; 5, 4; 14, 16, 10; 30, 40, 35, 20;
Links
- S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 237, K{B(n,3,-l)}).
Programs
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Maple
T:=proc(n,k) if k<=n then (k+1)*(n+2)*(2*n-k+3)*(n-k+1)/6 else 0 fi end: for n from 0 to 10 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form
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PARI
A107984_row(n)=vector(n+1,k,k*(2*n-k+4)*(n-k+2))*(n+2)/6 \\ M. F. Hasler, Dec 26 2016
Formula
T(n-2,k-1) = n*(2*n-k)*(n-k)*k/6. - M. F. Hasler, Dec 26 2016
G.f.: (1 + x - 4*x^2*y + x^3*y^2 + x^4*y^2)/((1 - x)^4*(1 - x*y)^4). - Stefano Spezia, Jul 11 2025
Comments