

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
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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^48x^2+15x16)/((x1)(x^47x^2+1)).
a(n) = a(n1) + 7*a(n2)  7*a(n3)  a(n4) + a(n5) 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}] (* JeanFrançois 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


AUTHOR

Creighton Dement, Apr 17 2005


STATUS

approved



