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1, 2, 2, 4, 3, 3, 6, 6, 4, 4, 9, 8, 8, 5, 5, 12, 12, 10, 6, 6, 16, 15, 15, 12, 12, 7, 7, 20, 20, 18, 18, 14, 14, 8, 8, 25, 24, 24, 21, 21, 16, 16, 9, 9, 30, 30, 28, 28, 24, 24, 18, 18, 10, 10
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums = the tetrahedral numbers, A000292, starting (1, 4, 10, 20, 35, 56, 84,...)
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FORMULA
| A128179 * A000012 as infinite lower triangular matrices.
Regarded as an array by antidiagonals A(i, j) = degree in q of q-Fibonacci number F(i+2, j-1) where F(1, k) = F(2, k) = 1, F(n, k) = F(n-1, k) + q^(n+k-2) * F(n-2, k). - Michael Somos Jun 08 2011
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EXAMPLE
| First few rows of the triangle are:
1;
2, 2;
4, 3, 3;
6, 6, 4, 4;
9, 8, 8, 5, 5;
12, 12, 10, 6, 6;
16, 15, 15, 12, 12, 7, 7;
...
First few rows of the array are:
1, 2, 3, 4, 5, 6, 7, 8, ...
2, 3, 4, 5, 6, 7, 8, 9, ...
4, 6, 8, 10, 12, 14, 16, 18, ...
6, 8, 10, 12, 14, 16, 18, 20, ...
9, 12, 15, 18, 21, 24, 27, 30, ...
...
A(3, 4) = 10 because F(5, 3) = 1 + q^4 + q^5 + q^6 + q^10. A(4, 4) = 12 because F(6, 3) = 1 + q^4 + q^5 + q^6 + q^7 + q^10 + q^11 + q^12.
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PROG
| (PARI) {T(n, k) = (n - k + 2)\2 * ((n + k + 1)\2)} /* Michael Somos Jun 08 2011 */
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CROSSREFS
| Cf. A128179, A000012, A000292.
Sequence in context: A205563 A147594 A205678 * A143228 A143211 A131052
Adjacent sequences: A128587 A128588 A128589 * A128591 A128592 A128593
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 11 2007
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