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A173031
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Sequence whose G.f is given by: 1/(1-z)/(1-2*z)^2/(1-z-z^2).
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0
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1, 6, 24, 79, 232, 632, 1633, 4058, 9788, 23063, 53332, 121452, 273089, 607534, 1339376, 2929951, 6366480, 13752880, 29556545, 63232370, 134731956, 286044711, 605326044, 1277246724, 2687879137, 5642847462, 11820387528, 24710992303
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..27.
Index to sequences with linear recurrences with constant coefficients, signature (6,-12,7,4,-4).
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FORMULA
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Recurrence formula: with the first values, a(n+5):=6*a(n+4)-12*a(n+3)+7*a(n+2)+4*a(n+1)-4*a(n). a(n)= (38/5*5^(1/2)+17)*((1+sqrt(5))/2)^n+(-38/5*5^(1/2)+17)*((1-sqrt(5))/2)^n-32*2^n-1+16*2^(n-1)*n. a(n)=F(n+8)+2^(n+3)*(n-4)-1, where (F(n)) is the Fibonacci sequence for which F(0)=F(1)=1, F(2)=2, aso (linked with A000045).
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EXAMPLE
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from f(z)=1+6z+24z^2+79z^3+232z^4+632z^5+1633z^6+4058z^7+9788z^8+23063z^9+53332z^10+121452z^11+273089z^12+607534z^13+... comes a(0)=1, a(6)=1633 for examples.
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MAPLE
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c(0):=1:c(1):=6:c(2):=24:c(3):=79:c(4):=232:for n from 0 to 30 do : c(n+5):=6*c(n+4)-12*c(n+3)+7*c(n+2)+4*c(n+1)-4*c(n): od :seq(c(n), n=0..30); taylor((-1/(-1+z)/(-1+2*z)^2/(1-z-z^2)), z=0, 30); for n from 0 to 30 do a(n):=simplify((38/5*5^(1/2)+17)*((1+sqrt(5))/2)^n+(-38/5*5^(1/2)+17)*((1-sqrt(5))/2)^n-32*2^n-1+16*2^(n-1)*n):od:seq(a(n), n=0..30);
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CROSSREFS
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Sequence in context: A058809 A140088 A011855 * A004404 A201189 A001788
Adjacent sequences: A173028 A173029 A173030 * A173032 A173033 A173034
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KEYWORD
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easy,nonn
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AUTHOR
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Richard Choulet, Feb 07 2010
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STATUS
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approved
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