

A103217


Hexagonal numbers triangle read by rows: T(n,k)=(n+1k)*(2*(n+1k)1).


1



1, 6, 1, 15, 6, 1, 28, 15, 6, 1, 45, 28, 15, 6, 1, 66, 45, 28, 15, 6, 1, 91, 66, 45, 28, 15, 6, 1, 120, 91, 66, 45, 28, 15, 6, 1, 153, 120, 91, 66, 45, 28, 15, 6, 1, 190, 153, 120, 91, 66, 45, 28, 15, 6, 1, 231, 190, 153, 120, 91, 66, 45, 28, 15, 6, 1, 276, 231, 190, 153, 120, 91, 66
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OFFSET

0,2


COMMENTS

The triangle is generated by the product A*B = B*A of the infinite lower triangular matrices A =
1 0 0 0...
1 1 0 0...
1 1 1 0...
1 1 1 1...
... and B =
1 0 0 0...
5 1 0 0...
9 5 1 0...
13 9 5 1...
...
The only prime hexagonal pyramidal number is 7. The only semiprime hexagonal pyramidal numbers are: 22, 95, 161. All greater hexagonal pyramidal numbers A002412 have at least 3 prime factors. Note that 7337 = 11 * 23 * 29 is a palindromatic 3brilliant number and 65941 = 23 * 47 * 61 is 3brilliant.  Jonathan Vos Post, Jan 26 2005


LINKS

Table of n, a(n) for n=0..72.
Jonathan Vos Post, Table of Polytope Numbers, Sorted, Through 1,000,000.
Eric Weisstein. Hexagonal Number.
Eric Weisstein. Hexagonal Pyramidal Number.


EXAMPLE

Triangle begins:
1,
6,1,
15,6,1,
28,15,6,1,
45,28,15,6,1,
66,45,28,15,6,1,
91,66,45,28,15,6,1,


MATHEMATICA

T[n_, k_] := (n + 1  k)*(2*(n + 1  k)  1); Flatten[ Table[ T[n, k], {n, 0, 10}, {k, 0, n}]] (* Robert G. Wilson v, Feb 10 2005 *)


PROG

(PARI) T(n, k) = (n+1k)*(2*(n+1k)1); for(i=0, 10, for(j=0, i, print1(T(i, j), ", ")); print())


CROSSREFS

Row sums give A002412 (hexagonal pyramidal numbers).
Cf. A000384, A002412.
Sequence in context: A146997 A147483 A050309 * A136273 A125233 A139727
Adjacent sequences: A103214 A103215 A103216 * A103218 A103219 A103220


KEYWORD

easy,nonn,tabl


AUTHOR

Lambert Klasen (lambert.klasen(AT)gmx.de) and Gary W. Adamson, Jan 25 2005


STATUS

approved



