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 A114197 A Pascal-Fibonacci triangle. 14
 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; text; internal format)
 OFFSET 0,5 COMMENTS T(2n,n) is A114198. Row sums are A114199. Row sums of inverse are 0^n. LINKS Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4. 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) = Sum_{j=0..n} C(k, j)C(n-k, n-j)F(k-j) if k <= n, 0 otherwise. 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); G.f.: -((x^2-x)*y-x+1)/((x^4+x^3-x^2)*y^2+(x^3-3*x^2+2*x)*y-x^2+2*x-1). - Vladimir Kruchinin, Jan 15 2018 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,   7,   1;   1,   8,  43, 106, 142, 106,  43,   8,   1; CROSSREFS Some other Fibonacci-Pascal triangles: A027926, A036355, A037027, A074829, A105809, A109906, A114197, A162741, A228074. Sequence in context: A166293 A094525 A130671 * A108350 A086617 A094526 Adjacent sequences:  A114194 A114195 A114196 * A114198 A114199 A114200 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Nov 16 2005 STATUS approved

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Last modified May 24 18:33 EDT 2020. Contains 334580 sequences. (Running on oeis4.)