A182193 Sequence of row differences related to table A182355.
-1, 1, 19, 125, 743, 4345, 25339, 147701, 860879, 5017585, 29244643, 170450285, 993457079, 5790292201, 33748296139, 196699484645, 1146448611743, 6681992185825, 38945504503219, 226991034833501, 1323000704497799, 7711013192153305, 44943078448422043
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (7,-7,1).
Programs
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Magma
I:=[-1,1]; [n le 2 select I[n] else 6*Self(n-1)-Self(n-2)+12: n in [1..30]]; // Vincenzo Librandi, Feb 10 2014
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Maple
Pell:= proc(n) option remember; if n<2 then n else 2*Pell(n-1) + Pell(n-2) fi; end: seq(Pell(2*n) + 2*Pell(2*n-1) - 3, n=0..40); # G. C. Greubel, May 24 2021 -
Mathematica
LinearRecurrence[{7,-7,1},{-1,1,19},30] (* Harvey P. Dale, Feb 09 2014 *) -
PARI
Vec(-(1-8*x-5*x^2)/((1-x)*(1-6*x+x^2)) + O(x^30)) \\ Colin Barker, Mar 05 2016
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Sage
[lucas_number2(2*n,2,-1) - lucas_number1(2*n,2,-1) - 3 for n in (0..40)] # G. C. Greubel, May 24 2021
Formula
a(n) = 6*a(n-1) - a(n-2) + 12.
a(0)=-1, a(1)=1, a(2)=19, a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3). - Harvey P. Dale, Feb 09 2014
From Colin Barker, Mar 05 2016: (Start)
a(n) = -3 + (1/4)*( (4-sqrt(2))*(3+2*sqrt(2))^n + (4+sqrt(2))*(3-2*sqrt(2))^n ).
G.f.: -(1-8*x-5*x^2) / ((1-x)*(1-6*x+x^2)).
(End)
Extensions
More terms from Harvey P. Dale, Feb 09 2014
Comments