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Search: id:A165999
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| A165999 |
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Triangle read by rows: T(0,0) = 1, T(n,k) = T(n-1,k-1) + T(n-1,k) for n > 0, 0 < k <= trinv(n), where trinv(n) = floor((1+sqrt(1+8*n))/2), and entries outside triangle are 0. |
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+0
1
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| 1, 1, 1, 1, 2, 1, 3, 2, 1, 4, 5, 1, 5, 9, 1, 6, 14, 9, 1, 7, 20, 23, 1, 8, 27, 43, 1, 9, 35, 70, 1, 10, 44, 105, 70, 1, 11, 54, 149, 175, 1, 12, 65, 203, 324, 1, 13, 77, 268, 527, 1, 14, 90, 345, 795, 1, 15, 104, 435, 1140, 795, 1, 16, 119, 539, 1575, 1935, 1, 17, 135, 658, 2114
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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There are trinv(n) terms in row n (see A002024). Related to A136730.
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EXAMPLE
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Triangle begins: [1] [1, 1] [1, 2] [1, 3, 2] [1, 4, 5] [1, 5, 9] [1, 6, 14, 9] [1, 7, 20, 23] [1, 8, 27, 43] [1, 9, 35, 70] [1, 10, 44, 105, 70] [1, 11, 54, 149, 175] [1, 12, 65, 203, 324] [1, 13, 77, 268, 527] [1, 14, 90, 345, 795] [1, 15, 104, 435, 1140, 795]
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PROGRAM
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(PARI) trinv(n) = floor((1+sqrt(1+8*n))/2); f(n) = trinv(n-1); s=19; M=matrix(s, s); for(n=1, s, M[n, 1]=1); for(n=2, s, for(k=2, f(n), M[n, k]=M[n-1, k-1]+M[n-1, k])); for(n=1, s, for(k=1, f(n), print1(M[n, k], ", ")))
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CROSSREFS
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A101482 (diagonal T(A000217(n), n))
Sequence in context: A152072 A105438 A062001 this_sequence A049280 A108786 A008315
Adjacent sequences: A165996 A165997 A165998 this_sequence A166000 A166001 A166002
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KEYWORD
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nonn,tabf
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AUTHOR
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Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Oct 03 2009
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