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Search: id:A103217
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| A103217 |
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Hexagonal numbers triangle read by rows: T(n,k)=(n+1-k)*(2*(n+1-k)-1). |
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+0
1
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| 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
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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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 3-brilliant number and 65941 = 23 * 47 * 61 is 3-brilliant. - Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 26 2005
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LINKS
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Jonathan Vos Post, Table of Polytope Numbers, Sorted, Through 1,000,000.
Eric Weisstein. Hexagonal Number.
Eric Weisstein. Hexagonal Pyramidal Number.
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EXAMPLE
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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,
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MATHEMATICA
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T[n_, k_] := (n + 1 - k)*(2*(n + 1 - k) - 1); Flatten[ Table[ T[n, k], {n, 0, 10}, {k, 0, n}]] (from Robert G. Wilson v Feb 10 2005)
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PROGRAM
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(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())
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CROSSREFS
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Row sums give A002412 (hexagonal pyramidal numbers)
Cf. A000384, A002412.
Sequence in context: A146997 A147483 A050309 this_sequence A136273 A125233 A139727
Adjacent sequences: A103214 A103215 A103216 this_sequence A103218 A103219 A103220
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Lambert Klasen (lambert.klasen(AT)gmx.de) and Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 25 2005
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