A215484
a(n) = 21*a(n-2) + 7*a(n-3), with a(0)=a(1)=0, a(2)=9.
Original entry on oeis.org
0, 0, 9, 0, 189, 63, 3969, 2646, 83790, 83349, 1778112, 2336859, 37923795, 61520823, 812757708, 1557403848, 17498557629, 38394784764, 378371537145, 928780383447, 8214565773393, 22152988812402, 179007343925382, 522714725474193, 3914225144119836, 12230060642435727, 85857731104835907, 284230849499989119
Offset: 0
We have a(5)=7*a(2), a(4)=21*a(2), a(4)=3*a(5), a(6)=21*a(4), a(7)=14*a(4), 3*a(7)=2*a(6), a(8)-a(9)=7*a(5), a(9)=21*a(6), 2*a(9)=63*a(7), a(12)=455*a(9) - especially the values and the relations connecting with a(8) and a(9) are very attractive.
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- R. Witula, D. Slota and A. Warzynski, Quasi-Fibonacci Numbers of the Seventh Order, J. Integer Seq., 9 (2006), Article 06.4.3.
- Index entries for linear recurrences with constant coefficients, signature (0, 21, 7).
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I:=[0,0,9]; [n le 3 select I[n] else 21*Self(n-2) +7*Self(n-3): n in [1..30]]; // G. C. Greubel, Apr 19 2018
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LinearRecurrence[{0,21,7}, {0,0,9}, 50]
CoefficientList[Series[9x^2/(1-21x^2-7x^3),{x,0,30}],x] (* Harvey P. Dale, Jul 06 2021 *)
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x='x+O('x^30); concat([0,0], Vec(9*x^2/(1-21*x^2-7*x^3))) \\ G. C. Greubel, Apr 19 2018
A215492
a(n) = 21*a(n-2) + 7*a(n-3), with a(0)=0, a(1)=3, and a(2)=6.
Original entry on oeis.org
0, 3, 6, 63, 147, 1365, 3528, 29694, 83643, 648270, 1964361, 14199171, 45789471, 311933118, 1060973088, 6871121775, 24463966674, 151720368891, 561841152579, 3357375513429, 12860706786396, 74437773850062, 293576471108319, 1653218198356074, 6686170310225133
Offset: 0
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Roman Witula, Damian Slota and Adam Warzynski, Quasi-Fibonacci Numbers of the Seventh Order, J. Integer Seq., 9 (2006), Article 06.4.3.
- Index entries for linear recurrences with constant coefficients, signature (0, 21, 7).
Cf.
A121458,
A215484,
A121449,
A085810,
A215404,
A077998,
A006054,
A033304,
A052975,
A094789,
A005021,
A121442,
A121458.
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I:=[0,3,6]; [n le 3 select I[n] else 21*Self(n-2)+7*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Sep 18 2015
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LinearRecurrence[{0,21,7}, {0,3,6}, 50]
CoefficientList[Series[(3 x + 6 x^2)/(1 - 21 x^2 - 7 x^3), {x, 0, 33}], x] (* Vincenzo Librandi, Sep 18 2015 *)
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concat(0,Vec((3+6*x)/(1-21*x^2-7*x^3)+O(x^99))) \\ Charles R Greathouse IV, Oct 01 2012
A271945
Expansion of 4*x^2/(1 - x - 9*x^2 + x^3).
Original entry on oeis.org
0, 0, 4, 4, 40, 72, 428, 1036, 4816, 13712, 56020, 174612, 665080, 2180568, 7991676, 26951708, 96696224, 331269920, 1174584228, 4059317284, 14299305416, 49658576744, 174293008204, 606920893484, 2125899390576, 7413894423728, 25940068045428, 90539218468404
Offset: 0
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[n le 2 select 2*n*(n-1) else Self(n)+9*Self(n-1)-Self(n-2): n in [0..30]];
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CoefficientList[Series[4 x^2 /(1 - x - 9 x^2 + x^3), {x, 0, 30}], x]
LinearRecurrence[{1,9,-1},{0,0,4},30] (* Harvey P. Dale, Jul 18 2021 *)
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x='x+O('x^99); concat([0, 0], Vec(4*x^2/(1-x-9*x^2+x^3))) \\ Altug Alkan, Apr 18 2016
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gf = 4*x^2/(1 - x - 9*x^2 + x^3); taylor(gf, x, 0, 30).list() # Bruno Berselli, Apr 18 2016
Showing 1-3 of 3 results.
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