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Search: id:A027023
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| A027023 |
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Tribonacci array: triangular array T read by rows: T(n,0)=1 for n >= 0, T(n,1)=T(n,2n)=1 for n >= 1, T(n,2)=1 for n >= 2 and for n >= 3, T(n,k)=T(n-1,k-3)+T(n-1,k-2)+T(n-1,k-1) for 3<=k<=2n-1. |
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28
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| 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 5, 5, 1, 1, 1, 1, 3, 5, 9, 13, 11, 1, 1, 1, 1, 3, 5, 9, 17, 27, 33, 25, 1, 1, 1, 1, 3, 5, 9, 17, 31, 53, 77, 85, 59, 1, 1, 1, 1, 3, 5, 9, 17, 31, 57, 101, 161, 215, 221, 145, 1, 1, 1, 1, 3, 5, 9, 17, 31, 57, 105, 189, 319, 477, 597, 581, 367, 1, 1, 1
(list; graph; listen)
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OFFSET
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1,8
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COMMENT
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The n-th row has 2n+1 terms. The array begins:
1
1,1,1
1,1,1,3,1
1,1,1,3,5,5,1
1,1,1,3,5,9,13,11,1
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MATHEMATICA
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T[n_, 0] := 1; T[n_, 1] := 1; T[n_, k_]/; (k==2n) := 1 /; n >=1; T[n_, 2] := 1; T[n_, k_]/; (k <= 2n-1) := T[n, k]=T[n-1, k-3]+T[n-1, k-2]+T[n-1, k-1].
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PROGRAM
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(PARI) T(n, k)=if(k<0|k>2*n, 0, if(k<3|k==2*n, 1, T(n-1, k-3)+T(n-1, k-2)+T(n-1, k-1))) - Michael Somos Feb 14 2004
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CROSSREFS
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Columns are essentially constant with values from A000213 (tribonacci numbers).
Diagonals T(n,n+c) are A027024 (c=2), A027025 (c=3), A027026 (c=4).
Diagonals T(n,2n-c) are A027050 (c=1), A027051 (c=2), A027027 (c=3), A027028 (c=4), A027029 (c=5), A027030 (c=6), A027031 (c=7), A027032 (c=8), A027033 (c=9), A027034 (c=10).
Many other sequences are derived from this one: see A027035 A027036 A027037 A027038 A027039 A027040 A027041 A027042 A027043 A027044 A027045 and
A027046 A027047 A027048 A027049.
Other arrays of this type: A027052, A027082, A027113.
Sequence in context: A029382 A073780 A124389 this_sequence A052371 A062278 A016465
Adjacent sequences: A027020 A027021 A027022 this_sequence A027024 A027025 A027026
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KEYWORD
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nonn,tabf,nice
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Edited by njas and Ralf Stephan, Feb 13 2004
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