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A039717
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Row sums of convolution triangle A030523.
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5
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1, 4, 15, 55, 200, 725, 2625, 9500, 34375, 124375, 450000, 1628125, 5890625, 21312500, 77109375, 278984375, 1009375000, 3651953125, 13212890625, 47804687500, 172958984375, 625771484375, 2264062500000, 8191455078125
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Number of (s(0), s(1), ..., s(2n)) such that 0 < s(i) < 10 and |s(i) - s(i-1)| = 1 for i = 1,2,....,2n, s(0) = 3, s(2n) = 5.
With offset 0 = INVERT transform of A001792: (1, 3, 8, 20, 48, 112,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 26 2010]
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LINKS
| W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
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FORMULA
| G.f.: x*(1-x)/(1-5*x+5*x^2)= g1(3, x)/(1-g1(3, x)), g1(3, x) := x*(1-x)/(1-2*x)^2 (G.f. first column of A030523).
Binomial transform of Fib(2n+2). a(n)=(sqrt(5)/2+5/2)^n(3sqrt(5)/10+1/2)-(5/2-sqrt(5)/2)^n(3sqrt(5)/10-1/2) - Paul Barry (pbarry(AT)wit.ie), Apr 16 2004
a(n)=(1/5)*Sum(r, 1, 9, Sin(3*r*Pi/10)Sin(r*Pi/2)(2Cos(r*Pi/10))^(2n)) a(n)=5a(n-1)-5a(n-2)
a(n)=sum{k=0..n, sum{i=0..n, C(n, i)C(k+i+1, 2k+1)}}. - Paul Barry (pbarry(AT)wit.ie), Jun 22 2004
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 01 2010: (Start)
Limit(a(n+k)/a(k), k=infinity) = (A020876(n) + A093131(n)*sqrt(5))/2
Limit(A020876(n)/A093131(n), n=infinity) = sqrt(5)
(End)
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CROSSREFS
| Cf. A000045.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jul 01 2010: (Start)
Appears in A109106.
(End)
Cf. A001792 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 26 2010]
Sequence in context: A102349 A126932 A094833 * A026013 A050183 A094375
Adjacent sequences: A039714 A039715 A039716 * A039718 A039719 A039720
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KEYWORD
| easy,nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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