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Search: id:A073154
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| 1, 2, 4, 5, 9, 14, 18, 28, 38, 56, 70, 106, 131, 167, 237, 293, 433, 523, 613, 753, 1046, 1283, 1869, 2219, 2543, 2893, 3479, 4762, 5808, 8374, 9839, 11099, 12359, 13824, 16390, 22198
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OFFSET
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0,2
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FORMULA
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Triangle {a(n, k), n >= 0, 0<=k<=n} defined by: a(0, 0)=1, a(n, 0)=A073157(n), a(n, n)=A073155(n+1), a(n, 0)=a(n-1, n-1) + a(n-2, n-2), a(n, k)=sum{j=0..k} A073157(j) * A073157(n-j).
G.f.: Sum_{n>=0, 0<=k<=n} a(n, k) x^n y^k = A(x*y)(A(x) - y A(x*y))/(1 - y) where A(x) = (1 - (1 - 4 x (1 + x)^2)^(1/2))/(2 x (1 + x)) is the ogf for A073157. - David Callan (callan(AT)stat.wisc.edu), Aug 16 2006
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EXAMPLE
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a(4,0)=a(3,3)+a(2,2)=56+14=70. a(5,2)=A073157(0)*A073157(5)+A073157(1)*A073157(4)+A073157(2)*A073157(3)= 1*293+2*70+5*18=523. Rows: {1}; {2,4}; {5,9,14}; {18,28,38,56}; {70,106,131,167,237}; {293,433,523,613,753,1046}; {1283,1869,2219,2543,2893,3479,4762};...
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CROSSREFS
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Cf. A073153, A073155, A073156, A073157, A073152.
Sequence in context: A162406 A129282 A073153 this_sequence A077882 A120939 A120770
Adjacent sequences: A073151 A073152 A073153 this_sequence A073155 A073156 A073157
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 29 2002
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