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A154999
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a(n) = 7*a(n-1) + 42*a(n-2), n>2; a(0)=1, a(1)=1, a(2)=13.
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6
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1, 1, 13, 133, 1477, 15925, 173509, 1883413, 20471269, 222402229, 2416608901, 26257155925, 285297665317, 3099884206069, 33681691385797, 365966976355477, 3976399872691813, 43205412115772725, 469446679463465221
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OFFSET
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0,3
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COMMENTS
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The sequences A155001, A155000, A154999, A154997 and A154996 have a common form: a(0)=a(1)=1, a(2)= 2*b+1, a(n) = (b+1)*(a(n-1) + b*a(n-2)), with b some constant. The generating function of these is (1 - b*x - b^2*x^2)/(1 - (b+1)*x - b*(1+b)*x^2). - R. J. Mathar, Jan 20 2009
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LINKS
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FORMULA
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a(n+1) = Sum_{k=0..n} A154929(n,k)*6^(n-k).
G.f.: (1 - 6*x - 36*x^2)/(1 - 7*x - 42*x^2). - G. C. Greubel, Apr 20 2021
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MATHEMATICA
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LinearRecurrence[{7, 42}, {1, 1, 13}, 31] (* G. C. Greubel, Apr 20 2021 *)
CoefficientList[Series[(1-6x-36x^2)/(1-7x-42x^2), {x, 0, 20}], x] (* Harvey P. Dale, Jan 14 2022 *)
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PROG
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(Magma) I:=[1, 13]; [1] cat [n le 2 select I[n] else 7*(Self(n-1) +6*Self(n-2)): n in [1..30]]; // G. C. Greubel, Apr 20 2021
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-6*x-36*x^2)/(1-7*x-42*x^2) ).list()
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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