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A144961
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Eigentriangle whose left border is the Padovan sequence, and whose right border and row sums are a modified Fibonacci sequence.
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1
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1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 1, 0, 0, 3, 1, 1, 0, 1, 0, 0, 5, 1, 1, 1, 0, 2, 0, 0, 8, 2, 1, 1, 1, 0, 3, 0, 0, 13, 2, 2, 1, 1, 2, 0, 5, 0, 0, 21, 3, 2, 2, 1, 2, 3, 0, 8, 0, 0, 34, 4, 3, 2, 2, 2, 3, 5, 0, 13, 0, 0, 55, 5, 4, 3, 2, 4, 3, 5
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,15
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COMMENTS
| Left border = A000931, the Padovan sequence: (1, 0, 0, 1, 0, 1, 1, 1, 2, 2,...).
Right border = (1, 1, 1, 1, 2, 3, 5, 8, 13, 21,...)
Row sums = (1, 1, 1, 2, 3, 5, 8, 13, 21, 34,...).
Sum of n-th row terms = rightmost term in next row.
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LINKS
| Nathaniel Johnston, Rows n = 0..150, flattened
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FORMULA
| Triangle read by rows, termwise products of a Padovan "decrescendo" triangle: (1; 0,1; 0,0,1; 1,0,0,1,...) and the Fibonacci series preceded by two 1's: (1, 1, 1, 1, 2, 3, 5, 8,...); (i.e. the INVERT transform of the Padovan sequence).
a(n,k) = fibonacci(max(k-1,1))*A000931(n-k). - Nathaniel Johnston, May 05 2011
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EXAMPLE
| First few rows of the triangle =
1
0 1
0 0 1
1 0 0 1
0 1 0 0 2
1 0 1 0 0 3
1 1 0 1 0 0 5
1 1 1 0 2 0 0 8
2 1 1 1 0 3 0 0 13
2 2 1 1 2 0 5 0 0 21
3 2 2 1 2 3 0 8 0 0 34
4 3 2 2 2 3 5 0 13 0 0 55
...
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MAPLE
| with(combinat): A000931 := proc(n) option remember: if(n=0)then return 1: elif(n<=2)then return 0: else return procname(n-2)+procname(n-3): fi: end: A144961 := proc(n, k) return fibonacci(max(k-1, 1))*A000931(n-k) end:for n from 0 to 12 do for k from 0 to n do printf("%d, ", A144961(n, k)); od: printf("\n"); od: # Nathaniel Johnston, May 05 2011
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CROSSREFS
| Cf. A000045, A000931.
Sequence in context: A116488 A145765 A157424 * A144627 A135929 A080733
Adjacent sequences: A144958 A144959 A144960 * A144962 A144963 A144964
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 27 2008
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EXTENSIONS
| Example triangle corrected by Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), May 05 2011
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