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A141070
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Number of primes in rows of Pascal-like triangles with index of asymmetry (y=3) and index of obliquely (z=0 or z=1).
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0
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0, 0, 1, 1, 1, 1, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,7
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COMMENTS
| Pascal-like triangle with index of asymmetry (y=3) and index of
obliqueness (z=0) read by rows with recurrence G(n, k): G(n, 0)=G(n+1,
n+1)=1, G(n+2, n+1)=2, G(n+3, n+1)=4, G(n+4, n+1)=8, G(n+5, k)=G(n+1,
k-1)+G(n+1,
k)+G(n+2, k)+G(n+3, k)+G(n+4, k) for k:=1..(n+1).
Pascal-like triangle with index of asymmetry(y=3) and index of obliqueness
(z=1) read by rows with recurrence G(n, k): G(n, n)=G(n+1, 0)=1, G(n+2,
1)=2, G(n+3, 2)=4, G(n+4, 3)=8, G(n+5, k)=G(n+1, k-3)+G(n+1, k-4)+G(n+2,
k-3)+G(n+3,
k-2)+G(n+4, k-1) for k=4..(n+4).
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LINKS
| Juri-Stepan Gerasimov, Stepan's triangles and Pascal's triangle are connected by the recurrence relation ...
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EXAMPLE
| Pascal-like triangle (y=3, z=0) begins:
If 1, then a(1)=0.
If 1 1, then a(2)=0.
If 1 2 1, then prime 2 and a(3)=1.
If 1 4 2 1, then prime 2 and a(4)=1.
If 1 8 4 2 1, then prime 2 and a(5)=1.
If 1 16 8 4 2 1, then prime 2 and a(6)=1.
If 1 31 17 8 4 2 1, then primes 2, 17, 31 and a(7)=3.
If 1 60 35 17 8 4 2 1, then primes 2, 17 and a(8)=2.
If 1 116 72 35 17 8 4 2 1, then primes 2, 17 and a(9)=2.
If 1 224 148 72 35 17 8 4 2 1, then primes 2, 17 and
a(10)=2.
If 1 432 303 149 72 35 17 8 4 2 1, then primes 2, 17, 149
and a(11)=3, etc.
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CROSSREFS
| Cf. A140998.
Sequence in context: A085034 A119323 A102299 * A163751 A067279 A096101
Adjacent sequences: A141067 A141068 A141069 * A141071 A141072 A141073
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KEYWORD
| nonn,uned
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AUTHOR
| Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 16 2008
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EXTENSIONS
| Partially edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 18 2008
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