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

0,2

Comments

Kekulé numbers for certain benzenoids. Column 0 yields A000330. Main diagonal yields A000292. Row sums yield A006414.

Links

Table of n, a(n) for n=0..56.

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)}).

Formula

T(n-2,k-1) = n*(2*n-k)*(n-k)*k/6. - M. F. Hasler, Dec 26 2016

Example

Triangle begins:
   1;
   5,  4;
  14, 16, 10;
  30, 40, 35, 20;

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

Prog

(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

Crossrefs

Cf. A000330, A000292, A006414.

Sequence in context: A344817 A094414 A158867 * A133178 A377626 A154225

Adjacent sequences: A107981 A107982 A107983 * A107985 A107986 A107987

Keyword

nonn,tabl

Author

Emeric Deutsch, Jun 12 2005

Status

approved