A105671 a(2n) = Lucas(2n+3)^2, a(2n+1) = Lucas(2n+1)^2.

16, 1, 121, 16, 841, 121, 5776, 841, 39601, 5776, 271441, 39601, 1860496, 271441, 12752041, 1860496, 87403801, 12752041, 599074576, 87403801, 4106118241, 599074576, 28143753121, 4106118241, 192900153616, 28143753121

Offset: 0

Author

Creighton Dement, Apr 17 2005

Keywords

• easy
• nonn

Comments

This sequence is related to several other sequences on squares. In reference to the link "Sequences in Context", (a(n)) = vessigcycseq. Note that the identity "vessigcyc = jessigcyc + lessigcyc + tessigcyc" holds.

Floretion Algebra Multiplication Program, FAMP Code: 1vessigcycseq[ + 4.75'i - .75'j - .25'k + 4.75i' - .75j' - .25k' - 1.75'ii' - 3.75'jj' + 4.25'kk' - .25'ij' + 1.25'ik' - .25'ji' + 2.75'jk' + 1.25'ki' + 2.75'kj' + 2.25e]

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,7,-7,-1,1).

Crossrefs

Cf. A081071.

Programs

Mathematica

a[n_?EvenQ] := LucasL[n+3]^2; a[n_?OddQ] := LucasL[n]^2; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Sep 28 2011 *)

PARI

Vec((16 - 15*x + 8*x^2 + x^4) / ((1 - x)*(1 - 3*x + x^2)*(1 + 3*x + x^2)) + O(x^40)) \\ Colin Barker, May 01 2019

Formula

G.f.: (-x^4-8x^2+15x-16)/((x-1)(x^4-7x^2+1)).

a(n) = a(n-1) + 7*a(n-2) - 7*a(n-3) - a(n-4) + a(n-5) for n>4. - Colin Barker, May 01 2019

a(n) = 2*A098149(n+2) +5*A001519(n+2)-2. - R. J. Mathar, Sep 11 2019