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Search: id:A103219
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| A103219 |
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Triangle read by rows: T(n,k)=(n+1-k)*(4*(n+1-k)^2-1)/3+2*k*(n+1-k)^2. |
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+0
3
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| 1, 10, 3, 35, 18, 5, 84, 53, 26, 7, 165, 116, 71, 34, 9, 286, 215, 148, 89, 42, 11, 455, 358, 265, 180, 107, 50, 13, 680, 553, 430, 315, 212, 125, 58, 15, 969, 808, 651, 502, 365, 244, 143, 66, 17, 1330, 1131, 936, 749, 574, 415, 276, 161, 74, 19, 1771, 1530, 1293
(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 B * A of the infinite lower triangular matrices 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,
10,3,
35,18,5,
84,53,26,7,
165,116,71,34,9,
286,215,148,89,42,11,
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MATHEMATICA
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T[n_, k_] := (n + 1 - k)*(4*(n + 1 - k)^2 - 1)/3 + 2*k*(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)=(n+1-k)*(4*(n+1-k)^2-1)/3+2*k*(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 A103220.
T(n, 0 = n*(4*n^2 - 1)/3 = A000447(n+1);
T(n+1, n)= 8*n+2 = A017089(n+1);
Cf. A103218 (for product A*B), A103220.
Sequence in context: A068608 A079670 A050100 this_sequence A111126 A165790 A077194
Adjacent sequences: A103216 A103217 A103218 this_sequence A103220 A103221 A103222
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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 26 2005
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