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A075156
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Binomial transform of pentanacci numbers A074048: a(n)=Sum(Binomial(n,k)*A074048(k),(k=0,..,n)).
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0
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5, 6, 10, 24, 70, 216, 664, 2008, 5998, 17808, 52770, 156360, 463492, 1374392, 4076222, 12090144, 35859742, 106359928, 315460168, 935639768, 2775057510, 8230670416, 24411730298, 72403913480, 214746249796, 636926269816
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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LINKS
| N. J. A. Sloane, Transforms
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FORMULA
| a(n)=6a(n-1)-13a(n-2)+14a(n-3)-7a(n-4)+2a(n-5), a(0)=5, a(1)=6, a(2)=10, a(3)=24, a(4)=70. G.f.: (5-24*x+39*x^2-28*x^3+7*x^4)/(1-6*x+13*x^2-14*x^3+7*x^4-2*x^5)
a(n) = term (1,5) in the 1x5 matrix [70,24,10,6,5] . [6,1,0,0,0; -13,0,1,0,0; 14,0,0,1,0; -7,0,0,0,1; 2,0,0,0,0]^n. - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 25 2008
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MAPLE
| M := Matrix(5, (i, j)-> if (i=j-1) then 1 elif j>1 then 0 else [6, -13, 14, -7, 2][i] fi); a := n -> (Matrix([[70, 24, 10, 6, 5]]).M^(n))[1, 5]; seq (a(n), n=0..50); - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 25 2008
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MATHEMATICA
| CoefficientList[Series[(5-24*x+39*x^2-28*x^3+7*x^4)/(1-6*x+13*x^2-14*x^3+7*x^4-2*x^5), {x, 0, 25}], x]
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CROSSREFS
| Cf. A074048.
Sequence in context: A056050 A035111 A035282 * A075904 A018834 A029943
Adjacent sequences: A075153 A075154 A075155 * A075157 A075158 A075159
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KEYWORD
| easy,nonn
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AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Sep 07 2002
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