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 palindromic 3-brilliant number and 65941 = 23 * 47 * 61 is 3-brilliant. - Jonathan Vos Post, Jan 26 2005
LINKS
Jonathan Vos Post, Table of Polytope Numbers, Sorted, Through 1,000,000.
Eric Weisstein's World of Mathematics, Hexagonal Number.
Eric Weisstein's World of Mathematics, 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+1-k)*(2*(n+1-k)-1); for(i=0, 10, for(j=0, i, print1(T(i, j), ", ")); print())
CROSSREFS
KEYWORD
AUTHOR
Lambert Klasen (lambert.klasen(AT)gmx.de) and Gary W. Adamson, Jan 25 2005
STATUS
approved