

A008867


Triangle of truncated triangular numbers: kth term in nth row is number of dots in hexagon of sides k, nk, k, nk, k, nk.


7



1, 3, 3, 6, 7, 6, 10, 12, 12, 10, 15, 18, 19, 18, 15, 21, 25, 27, 27, 25, 21, 28, 33, 36, 37, 36, 33, 28, 36, 42, 46, 48, 48, 46, 42, 36, 45, 52, 57, 60, 61, 60, 57, 52, 45, 55, 63, 69, 73, 75, 75, 73, 69, 63, 55, 66, 75, 82, 87, 90, 91, 90, 87, 82, 75, 66, 78, 88, 96, 102, 106, 108, 108, 106, 102, 96, 88, 78
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OFFSET

2,2


COMMENTS

Closely related to A109439. The current sequence is made of truncated triangular numbers, the latter gives the full description. Both can help to build a cube with layers perpendicular to the great diagonal. E.g.: 15,18,19,18,15 in A008867 is a truncation of the lesser triangular numbers of 1,3,6,10,15,18,19,18,15,10,6,3,1 in A109439.  M. Dauchez (mdzzdm(AT)yahoo.fr), Sep 02 2005


LINKS

Hugo Pfoertner, Table of n, a(n) for n = 2..1226, rows 1..50, flattened.
J. H. Conway and N. J. A. Sloane, LowDimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 23692389 (pdf).


FORMULA

T(n,k) = n*(n3)/2  k^2 + k*n + 1.


MAPLE

T:= (n, k)> n*(n3)/2  k^2+k*n+1:
seq(seq(T(n, k), k=1..n1), n=2..14);


MATHEMATICA

T[n_, k_] := n*(n3)/2  k^2 + k*n + 1; Table[T[n, k], {n, 3, 20}, {k, n, 2, 1}] // Flatten (* Amiram Eldar, Dec 12 2018 *)


CROSSREFS

Row sums are A005900(n1).
Cf. A109439.
Sequence in context: A243307 A021301 A016652 * A185958 A273062 A269170
Adjacent sequences: A008864 A008865 A008866 * A008868 A008869 A008870


KEYWORD

nonn,tabl,easy


AUTHOR

N. J. A. Sloane, J. H. Conway and R. K. Guy


STATUS

approved



