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

0,3

Comments

Binomial transform of A093968.

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).

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).

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 *)

Prog

(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
(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
(Sage) [n*lucas_number1(n, 2, -1) for n in (0..30)] # G. C. Greubel, Dec 28 2021

Crossrefs

Cf. A000129, A006645, A023607, A093835.

Sequence in context: A240333 A227099 A225976 * A052201 A320460 A178704

Adjacent sequences: A093964 A093965 A093966 * A093968 A093969 A093970

Keyword

easy,nonn

Author

Paul Barry, Apr 21 2004

Status

approved