A213472 Period 20, repeat [1, 4, 0, 9, 1, 6, 4, 5, 9, 6, 6, 9, 5, 4, 6, 1, 9, 0, 4, 1].

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

Offset

0,2

Comments

Units digits of the centered triangular numbers A005448(n).

The cyclic part of this sequence is palindromic.

Links

Table of n, a(n) for n=0..85.

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) = A010879(A005448(n)).

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

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

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 - Sum_{i=1..19} a(n-i), with n > 19.

a(n) = (3n^2/2+3n/2+1) mod 10.

G.f.: (1+x+x^2)*(1+3*x-4*x^2+10*x^3-5*x^4+5*x^6-5*x^8+10*x^9-4*x^10+3*x^11+x^12) / ((1-x)*(1+x^2)*(1+x+x^2+x^3+x^4)*(1-x^2+x^4-x^6+x^8)). - Bruno Berselli, Jun 13 2012

Example

As the seventh centered triangular number is A005448(7)=64, which has units’ digit 4, then a(7)=4

Mathematica

Mod[1/2(3#^2-3#+2), 10] &/@Range[86]

Prog

(PARI) a(n)=(3*n^2+3*n+2)/2%10 \\ Charles R Greathouse IV, Jul 21 2015

Crossrefs

Cf. A010879, A005448.

Sequence in context: A306954 A187606 A138478 * A305742 A199000 A339530

Adjacent sequences: A213469 A213470 A213471 * A213473 A213474 A213475

Keyword

nonn,easy

Author

Ant King, Jun 12 2012

Status

approved