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A114197
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A Pascal-Fibonacci triangle.
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2
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 7, 4, 1, 1, 5, 13, 13, 5, 1, 1, 6, 21, 31, 21, 6, 1, 1, 7, 31, 61, 61, 31, 7, 1, 1, 8, 43, 106, 142, 106, 43, 8, 1, 1, 9, 57, 169, 286, 286, 169, 57, 9, 1, 1, 10, 73, 253, 520, 659, 520, 253, 73, 10, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| T(2n,n) is A114198. Row sums are A114199. Row sums of inverse are 0^n.
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REFERENCES
| Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.
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FORMULA
| As a number triangle, T(n, k)=sum{j=0..n-k, C(n-k, j)C(k, j)F(j)}; As a number triangle, T(n, k)=sum{j=0..n, C(n-k, n-j)C(k, j-k)F(j-k)}; As a number triangle, T(n, k)=if(k<=n, sum{j=0..n, C(k, j)C(n-k, n-j)F(k-j)}, 0); As a square array, T(n, k)=sum{j=0..n, C(n, j)C(k, j)F(j)}; As a square array, T(n, k)=sum{j=0..n+k, C(n, n+k-j)C(k, j-k)F(j-k)}; Column k has g.f. sum{j=0..k, C(k, j)F(j+1)(x/(1-x))^j}x^k/(1-x);
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EXAMPLE
| Triangle begins
1;
1, 1;
1, 2, 1;
1, 3, 3, 1;
1, 4, 7, 4, 1;
1, 5, 13, 13, 5, 1;
1, 6, 21, 31, 21, 6, 1;
1, 7, 31, 61, 61, 31, 6, 1;
1, 8, 43,106,142,106, 43, 8, 1;
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CROSSREFS
| Sequence in context: A166293 A094525 A130671 * A108350 A086617 A094526
Adjacent sequences: A114194 A114195 A114196 * A114198 A114199 A114200
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Nov 16 2005
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