A194826 Units' digits of the nonzero 9-gonal (nonagonal) numbers.

1, 9, 4, 6, 5, 1, 4, 4, 1, 5, 6, 4, 9, 1, 0, 6, 9, 9, 6, 0, 1, 9, 4, 6, 5, 1, 4, 4, 1, 5, 6, 4, 9, 1, 0, 6, 9, 9, 6, 0, 1, 9, 4, 6, 5, 1, 4, 4, 1, 5, 6, 4, 9, 1, 0, 6, 9, 9, 6, 0, 1, 9, 4, 6, 5, 1, 4, 4, 1, 5, 6, 4, 9, 1, 0, 6, 9, 9, 6, 0, 1, 9, 4, 6, 5, 1

Offset

1,2

Comments

This is a periodic sequence with period 20 and cycle 1, 9, 4, 6, 5, 1, 4, 4, 1, 5, 6, 4, 9, 1, 0, 6, 9, 9, 6, 0.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

Formula

a(n) = a(n-20).

a(n) = a(n-5) - a(n-10) + a(n-15).

a(n) = 45 - a(n-1) - a(n-2) - a(n-3) - a(n-4) - a(n-10) - a(n-11) - a(n-12) - a(n-13) - a(n-14).

a(n) = 90 - a(n-1) - a(n-2) - a(n-3) - ... - a(n-17) - a(n-18) - a(n-19).

a(n) = (1/2 n(7n-5)) mod 10.

G.f.: x*(1+9*x+4*x^2+6*x^3+5*x^4-5*x^6-5*x^8+6*x^10+9*x^11+9*x^12+6*x^13)/((1-x)*(1+x^2)*(1+x+x^2+x^3+x^4)*(1-x^2+x^4-x^6+x^8)). - Bruno Berselli, Sep 05 2011

a(n) = A010879(A001106(n)). - Michel Marcus, Aug 11 2015

Example

The seventh nonzero 9-gonal (nonagonal) number is A001106(7)=154, which has units' digit 4. Hence a(7)=4.

Mathematica

Table[Mod[n*(7*n-5)/2, 10], {n, 86}]

Prog

(Magma) [(Floor(n*(7*n-5)/2)) mod (10): n in [1..80]]; // Vincenzo Librandi, Sep 06 2011

Crossrefs

Cf. A001106, A010879.

Sequence in context: A343199 A139720 A248177 * A309610 A198989 A255013

Adjacent sequences: A194823 A194824 A194825 * A194827 A194828 A194829

Keyword

nonn,easy,base

Author

Ant King, Sep 04 2011

Status

approved