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A155130
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a(n) = 7*a(n-1) + 7*a(n-2), n>2, a(0)=1, a(1)=6, a(2)=48.
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10
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1, 6, 48, 378, 2982, 23520, 185514, 1463238, 11541264, 91031514, 718009446, 5663286720, 44669073162, 352326519174, 2778969146352, 21919069658682, 172886271635238, 1363637389057440, 10755665624848746, 84835121097343302
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OFFSET
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0,2
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,7).
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FORMULA
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G.f.: (1-x-x^2)/(1-7*x-7*x^2) .
a(n) = 3*( ((7 + sqrt(77))/2)^(n-1) + ((7 - sqrt(77))/2)^(n-1) ) + (27/77)*sqrt(77)*( ((7 + sqrt(77))/2)^(n-1) - ((7 - sqrt(77))/2)^(n-1) ) + (1/7)*[binomial(2*n,n) mod 2], with n>=0. - Paolo P. Lava, Jan 26 2009
a(n) = (1/7)*[n=0] - 6*(sqrt(7)*i)^(n-2)*ChebyshevU(n, -sqrt(7)*i/2). - G. C. Greubel, Mar 25 2021
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MAPLE
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m:= 7; 1, seq(simplify((1-m)*(sqrt(m)*I)^(n-2)*ChebyshevU(n, -I*sqrt(m)/2)), n = 1..30); # G. C. Greubel, Mar 25 2021
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MATHEMATICA
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LinearRecurrence[{7, 7}, {1, 6, 48}, 30] (* Harvey P. Dale, Mar 11 2018 *)
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PROG
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(Magma) m:=7; [1] cat [n le 2 select (m-1)*(m*n-(m-1)) else m*(Self(n-1) + Self(n-2)): n in [1..30]]; // G. C. Greubel, Mar 25 2021
(Sage) m=7; [1]+[-(m-1)*(sqrt(m)*i)^(n-2)*chebyshev_U(n, -sqrt(m)*i/2) for n in (1..30)] # G. C. Greubel, Mar 25 2021
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CROSSREFS
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Sequences of the form a(n) = m*(a(n-1) + a(n-2)) with a(0)=1, a(1) = m-1, a(2) = m^2 -1: A155020 (m=2), A155116 (m=3), A155117 (m=4), A155119 (m=5), A155127 (m=6), this sequence (m=7), A155132 (m=8), A155144 (m=9), A155157 (m=10).
Sequence in context: A326888 A326895 A291033 * A250164 A264083 A083233
Adjacent sequences: A155127 A155128 A155129 * A155131 A155132 A155133
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KEYWORD
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nonn
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AUTHOR
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Philippe Deléham, Jan 20 2009
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STATUS
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approved
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