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Search: id:A123315
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| A123315 |
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Pascrabble triangle, read by rows. |
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+0
1
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| 1, 3, 3, 8, 10, 8, 9, 12, 12, 9, 4, 15, 19, 15, 4, 7, 15, 19, 19, 15, 7, 8, 18, 19, 21, 19, 18, 8, 9, 22, 20, 11, 11, 20, 22, 9, 4, 15, 17, 15, 18, 15, 17, 15, 4, 7, 15, 18, 18, 20, 20, 18, 18, 15, 7, 8, 18, 20, 22, 21, 11, 21, 22, 20, 18, 8, 9, 22, 21, 17, 19, 18, 18, 19, 17, 21, 22, 9
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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The apex of the triangle is 1. Any other value is the Scrabble value of English name for the number which is the sum of the numbers above. This is generated the same way as A007318 Pascal's triangle read by rows, except apply A113172 to each sum. The first column of this triangle is 1, 3, 8, 9, 4, 7, 8, 9, 4, 7, 8, 9, 4, 7... = iterations 1, A113172(1), A113172(A113172(1)), A113172(A113172(A113172(1))). The central pascrabble numbers T(2n+1,n) = 1, 10, 19, 21, 18, 11, 22, ...
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FORMULA
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T(1,1) = 1; for i > 1, T(i,j) = A113172(T(i-1, j-1)+T(i-1, j).
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EXAMPLE
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Triangle begins:
row.|.values in row
.1..|01
.2..|03.03
.3..|08.10.08
.4..|09.12.12.09
.5..|04.15.19.15.04
.6..|07.15.19.19.15.07
.7..|08.18.19.21.19.18.08
.8..|09.22.20.11.11.20.22.09
.9..|04.15.17.15.18.15.17.15.04
10..|07.15.18.18.20.20.18.18.15.07
11..|08.18.20.22.21.11.21.22.20.18.8
12..|09.22.21.17.19.18.18.19.17.21.22.09
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CROSSREFS
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Cf. A007318 Pascal's triangle read by rows, A113172.
Adjacent sequences: A123312 A123313 A123314 this_sequence A123316 A123317 A123318
Sequence in context: A092481 A099508 A141577 this_sequence A052407 A105039 A090597
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KEYWORD
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easy,nonn,tabl,word
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 08 2006
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