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A103245
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Triangle read by rows: T(n,k)=binomial(2n+1,n-k)fibonacci(2k+1), (0<=k<=n).
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1
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1, 3, 2, 10, 10, 5, 35, 42, 35, 13, 126, 168, 180, 117, 34, 462, 660, 825, 715, 374, 89, 1716, 2574, 3575, 3718, 2652, 1157, 233, 6435, 10010, 15015, 17745, 15470, 9345, 3495, 610, 24310, 38896, 61880, 80444, 80920, 60520, 31688, 10370, 1597, 92378
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| S. G. Guba, Problem No. 174, Issue No. 4, JUly-August 1965, p. 73 of Matematika v Skole,
Problem H-77, The Fibonacci Quarterly, 5, No. 3, 1967, 256-258.
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FORMULA
| T(n, k)=binomial(2n+1, n-k)fibonacci(2k+1), (0<=k<=n).
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EXAMPLE
| Triangle begins:
1;
3,2;
10,10,5;
35,42,35,13;
126,168,180,117,34;
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MAPLE
| with(combinat): T:=(n, k)->binomial(2*n+1, n-k)*fibonacci(2*k+1): for n from 0 to 9 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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CROSSREFS
| Column 0 is A001700. Column 1 is A024483. T(n, n)=A001519(n) (the odd-subscripted Fibonacci numbers). Row sums are the powers of 5 (A000351). Alternating row sums yield A054108.
Sequence in context: A063549 A071653 A056861 * A019242 A064367 A113980
Adjacent sequences: A103242 A103243 A103244 * A103246 A103247 A103248
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KEYWORD
| nonn,tabl
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 19 2005
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