A093967 a(n) = n * Pell(n).
0, 1, 4, 15, 48, 145, 420, 1183, 3264, 8865, 23780, 63151, 166320, 434993, 1130948, 2925375, 7533312, 19323713, 49395780, 125877071, 319888560, 810893265, 2050891876, 5176349663, 13040153280, 32793453025, 82337215012, 206424991215
Offset: 0
Links
- Harry J. Smith, Table of n, a(n) for n = 0..1000
- Rigoberto Flórez, Robinson Higuita and Alexander Ramírez, The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials, arXiv:1808.01264 [math.NT], 2018.
- Index entries for linear recurrences with constant coefficients, signature (4,-2,-4,-1).
Programs
-
Magma
I:=[0,1,4,15]; [n le 4 select I[n] else 4*Self(n-1)-2*Self(n-2)-4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 20 2015
-
Maple
seq(fibonacci(n,2)*n, n=0..27); # Zerinvary Lajos, Apr 05 2008
-
Mathematica
LinearRecurrence[{4,-2,-4,-1}, {0,1,4,15}, 30] (* Vincenzo Librandi, Dec 20 2015 *) -
PARI
{ default(realprecision, 100); s=sqrt(2); for (n=0, 100, a=n*round(((1+s)^n-(1-s)^n)/(2*s)); write("b093967.txt", n, " ", a); ) } \\ Harry J. Smith, Jun 17 2009 -
Sage
[n*lucas_number1(n,2,-1) for n in (0..30)] # G. C. Greubel, Dec 28 2021
Formula
G.f.: x*(1+x^2)/(1 - 2*x - x^2)^2;
a(n) = n*((1+sqrt(2))^n - (1-sqrt(2))^n)/(2*sqrt(2));
a(n) = n * A000129(n).
Comments