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A105671 a(2n) = Lucas(2n+3)^2, a(2n+1) = Lucas(2n+1)^2. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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.

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).

FORMULA

Expansion of (-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

MATHEMATICA

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

PROG

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]

(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

CROSSREFS

Cf. A081071.

Sequence in context: A036179 A309132 A099923 * A145828 A223518 A095876

Adjacent sequences:  A105668 A105669 A105670 * A105672 A105673 A105674

KEYWORD

easy,nonn,changed

AUTHOR

Creighton Dement, Apr 17 2005

STATUS

approved

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Last modified September 20 13:59 EDT 2019. Contains 327238 sequences. (Running on oeis4.)