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A199512
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Triangle T(n,k) = Fibonacci(n+k+1), related to A000045 (Fibonacci numbers).
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2
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1, 1, 2, 2, 3, 5, 3, 5, 8, 13, 5, 8, 13, 21, 34, 8, 13, 21, 34, 55, 89, 13, 21, 34, 55, 89, 144, 233, 21, 34, 55, 89, 144, 233, 377, 610, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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Michel Marcus, Rows n=0..50 of triangle, flattened
László Németh, On the Binomial Interpolated Triangles, Journal of Integer Sequences, Vol. 20 (2017), Article 17.7.8. See p. 15.
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FORMULA
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T(n,k) = T(n,k-1) + T(n-1,k-1) = T(n-1,k-1) + T(n-1,k).
T(n,0) = Fibonacci(n+1) = A000045(n+1).
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EXAMPLE
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Triangle begins :
1
1, 2
2, 3, 5
3, 5, 8, 13
5, 8, 13, 21, 34
8, 13, 21, 34, 55, 89
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PROG
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(PARI) T(n, k) = fibonacci(n+k+1);
tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print); \\ Michel Marcus, Aug 01 2017
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CROSSREFS
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Cf. A000045, A199334.
Rows sums : A096140, Diagonal sums : A128620.
Sequence in context: A067330 A202874 A355197 * A303969 A304931 A304669
Adjacent sequences: A199509 A199510 A199511 * A199513 A199514 A199515
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Philippe Deléham, Nov 07 2011
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EXTENSIONS
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More terms from Michel Marcus, Aug 01 2017
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STATUS
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approved
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