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Search: id:A103218
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| A103218 |
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Triangle read by rows: T(n, k) = (2*k+1)*(n+1-k)^2. |
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+0
2
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| 1, 4, 3, 9, 12, 5, 16, 27, 20, 7, 25, 48, 45, 28, 9, 36, 75, 80, 63, 36, 11, 49, 108, 125, 112, 81, 44, 13, 64, 147, 180, 175, 144, 99, 52, 15, 81, 192, 245, 252, 225, 176, 117, 60, 17, 100, 243, 320, 343, 324, 275, 208, 135, 68, 19, 121, 300, 405, 448, 441, 396, 325, 240
(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 from the product A * B of the infinite lower triangular matrix A =
1 0 0 0...
3 1 0 0...
5 3 1 0...
7 5 3 1...
... and B =
1 0 0 0...
1 3 0 0...
1 3 5 0...
1 3 5 7...
...
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EXAMPLE
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Triangle begins:
1,
4,3,
9,12,5,
16,27,20,7,
25,48,45,28,9,
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MATHEMATICA
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T[n_, k_] := (2*k + 1)*(n + 1 - k)^2; 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) = (2*k+1)*(n+1-k)^2; 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).
T(n, 0)=A000290(n+1) (the squares);
T(n, 1)=3*n^2=A033428(n);
T(n, 2)=5*n^2=A033429(n+1);
T(n, 3)=7*n^2=A033582(n+2);
Cf. A103219 (product B*A), A002412, A000290.
Sequence in context: A094885 A094728 A131805 this_sequence A107381 A132192 A147756
Adjacent sequences: A103215 A103216 A103217 this_sequence A103219 A103220 A103221
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KEYWORD
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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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