OFFSET
0,1
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..2388
Index entries for linear recurrences with constant coefficients, signature (4,-3,-2,1).
FORMULA
Binomial transform of trace(A^n)/4, where A is the adjacency matrix of path graph P_4 (A005248 with interpolated zeros). - Paul Barry, Apr 24 2004
From George F. Johnson, Feb 04 2013: (Start)
G.f.: (1-x)*(2-4*x-x^2)/ ( (1-x-x^2)*(1-3*x+x^2) ).
a(n) = 4*a(n-1) - 3*a(n-2) - 2*a(n-3) + a(n-4) for n>3. (End)
EXAMPLE
a(8) = (L(8) + L(2 * 8)) / 2 = (47 + 2207) / 2 = 2254 / 2 = 1127. - Indranil Ghosh, Feb 06 2017
MATHEMATICA
LinearRecurrence[{4, -3, -2, 1}, {2, 2, 5, 11}, 30] (* Harvey P. Dale, Nov 22 2015 *)
Table[(LuasL[n] + LucasL[2*n])/2, {n, 0, 30}] (* G. C. Greubel, Dec 02 2017 *)
PROG
(PARI) x='x+O('x^30); Vec((1-x)*(2-4*x-x^2)/ ( (1-x-x^2)*(1-3*x+x^2) )) \\ G. C. Greubel, Dec 02 2017
(Magma) [(Lucas(n) + Lucas(2*n)/2: n in [0..30]]; // G. C. Greubel, Dec 02 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved