OFFSET
0,1
COMMENTS
Column sums of A245960.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Sandi Klavzar, Michel Mollard and Marko Petkovsek, The degree sequence of Fibonacci and Lucas cubes, Discrete Math., Vol. 311, No. 14 (2011), pp. 1310-1322.
Index entries for linear recurrences with constant coefficients, signature (3,-1).
FORMULA
G.f.: (2-x)*(1+x^2)/(1-3*x+x^2).
a(n) = 3*F(2n+1) = 3*A001519(n+1) = A022086(2n+1) for n>=2; F(n) = A000045(n) are the Fibonacci numbers.
a(n) = F(n-1)^2 + F(n)^2 + F(n+1)^2 + F(n+2)^2 for n > 1, where F(n) is the n-th Fibonacci number (A000045). - Amiram Eldar, Jan 11 2022
MAPLE
g := (2-x)*(1+x^2)/(1-3*x+x^2): gser := series(g, x = 0, 35): seq(coeff(gser, x, n), n = 0 .. 32);
with(combinat): 2, 5, seq(3*fibonacci(2*n+1), n = 2 .. 32);
MATHEMATICA
CoefficientList[Series[(2 - x)*(1 + x^2)/(1 - 3 x + x^2), {x, 0, 50}], x] (* G. C. Greubel, Oct 19 2017 *)
Join[{2, 5}, LinearRecurrence[{3, -1}, {15, 39}, 30]] (* Vincenzo Librandi, Oct 19 2017 *)
PROG
(PARI) my(x='x+O('x^50)); Vec((2-x)*(1+x^2)/(1-3x+x^2)) \\ G. C. Greubel, Oct 19 2017
(Magma) I:=[2, 5, 15, 39]; [n le 4 select I[n] else 3*Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 19 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 23 2015
STATUS
approved