A194599 Units' digits of the nonzero hexagonal numbers.

1, 6, 5, 8, 5, 6, 1, 0, 3, 0, 1, 6, 5, 8, 5, 6, 1, 0, 3, 0, 1, 6, 5, 8, 5, 6, 1, 0, 3, 0, 1, 6, 5, 8, 5, 6, 1, 0, 3, 0, 1, 6, 5, 8, 5, 6, 1, 0, 3, 0, 1, 6, 5, 8, 5, 6, 1, 0, 3, 0, 1, 6, 5, 8, 5, 6, 1, 0, 3, 0, 1, 6, 5, 8, 5, 6, 1, 0, 3, 0, 1, 6, 5, 8, 5, 6, 1, 0, 3, 0, 1, 6, 5, 8, 5, 6, 1, 0, 3, 0

Offset

1,2

Comments

This is a periodic sequence with period 10 and cycle 1, 6, 5, 8, 5, 6, 1, 0, 3, 0.

As the sum of the terms contained in each cycle is 35 they also satisfy the ninth-order inhomogeneous recurrence a(n)=35-a(n-1)-a(n-2)-a(n-3)-a(n-4)-a(n-5)-a(n-6)-a(n-7)-a(n-8)-a(n-9).

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = a(n-10).

a(n) = (n*(2*n-1)) mod 10.

G.f. -x*(1+6*x+5*x^2+8*x^3+5*x^4+6*x^5+x^6+3*x^8) / ( (x-1)*(1+x)*(x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1) ). - R. J. Mathar, Aug 30 2011

a(n) = A010879(A000384(n)). - Michel Marcus, Aug 10 2015

Example

The seventh nonzero hexagonal number is A000384(7)=91, which has units' digit 1. Hence a(7)=1.

Mathematica

Mod[# (2#-1), 10] &/@Range[100]
Mod[PolygonalNumber[6, Range[100]], 10] (* Harvey P. Dale, Oct 04 2024 *)

Crossrefs

Cf. A000384, A010879.

Sequence in context: A225113 A329247 A133618 * A253300 A339253 A335165

Adjacent sequences: A194596 A194597 A194598 * A194600 A194601 A194602

Keyword

nonn,easy,base

Author

Ant King, Aug 30 2011

Status

approved