A235944 Digital roots of squares of Lucas numbers.

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

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 A353770 A049762

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