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A102036
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Triangle, read by rows, where the terms are generated by the rule: T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k-1) + T(n-3,k-1), with T(0,0)=1.
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1
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1, 1, 1, 1, 3, 1, 1, 6, 5, 1, 1, 9, 15, 7, 1, 1, 12, 33, 28, 9, 1, 1, 15, 60, 81, 45, 11, 1, 1, 18, 96, 189, 161, 66, 13, 1, 1, 21, 141, 378, 459, 281, 91, 15, 1, 1, 24, 195, 675, 1107, 946, 449, 120, 17, 1, 1, 27, 258, 1107, 2349, 2673, 1742, 673, 153, 19, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums form A077939. This sequence was inspired by Luke Hanna.
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EXAMPLE
| Generated by adding preceding terms in the triangle
at positions that form the letter 'L': T(n,k) =
T(n-3,k-1) +
T(n-2,k-1) +
T(n-1,k-1) + T(n-1,k).
Rows begin:
[1],
[1,1],
[1,3,1],
[1,6,5,1],
[1,9,15,7,1],
[1,12,33,28,9,1],
[1,15,60,81,45,11,1],
[1,18,96,189,161,66,13,1],
[1,21,141,378,459,281,91,15,1],...
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PROG
| (PARI) {T(n, k)=if(n<k|k<0, 0, if(n==0, 1, T(n-1, k)+T(n-1, k-1)+T(n-2, k-1)+T(n-3, k-1)))}
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CROSSREFS
| Cf. A077939.
Sequence in context: A128101 A124802 A178867 * A121524 A103141 A129818
Adjacent sequences: A102033 A102034 A102035 * A102037 A102038 A102039
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Dec 30 2004
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