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A235944 Digital roots of squares of Lucas numbers. 0
4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1, 4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1, 4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1, 4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1, 4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1, 4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1, 4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1, 4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1, 4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The sequence is periodic with period 12.

LINKS

Table of n, a(n) for n=0..107.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

FORMULA

a(n) = A010888(A001254(n)).

a(n) = a(n-12).

G.f.: -(x^11 +9*x^10 +7*x^9 +4*x^8 +4*x^7 +9*x^6 +4*x^5 +4*x^4 +7*x^3 +9*x^2 +x +4) / (x^12 -1).

EXAMPLE

a(5)=4 because A000032[5]=11 and the digital root of 11*11 = 121 is 4.

MATHEMATICA

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1}, 108] (* Ray Chandler, Aug 27 2015 *)

PadRight[{}, 120, {4, 1, 9, 7, 4, 4, 9, 4, 4, 7, 9, 1}] (* Harvey P. Dale, Feb 18 2018 *)

PROG

(PARI)

Vec(-(x^11+9*x^10+7*x^9+4*x^8+4*x^7+9*x^6+4*x^5+4*x^4+7*x^3+9*x^2+x+4)/(x^12-1) + O(x^100))

CROSSREFS

Cf. A000032, A001254, A216676.

Sequence in context: A325012 A092162 A073056 * A299615 A049762 A105495

Adjacent sequences:  A235941 A235942 A235943 * A235945 A235946 A235947

KEYWORD

nonn,easy,base

AUTHOR

Colin Barker, Jan 17 2014

EXTENSIONS

Extended by Ray Chandler, Aug 27 2015

STATUS

approved

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Last modified December 11 23:44 EST 2019. Contains 329945 sequences. (Running on oeis4.)