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A205651 Period 6: repeat (1, 6, 5, 4, 9, 0). 0
1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The members of this sequence are also the units' digits of the indices of those non-zero square numbers that are also triangular.

The coefficients of x^n in the numerator of the generating function form the periodic cycle of the sequence.

LINKS

Table of n, a(n) for n=1..86.

Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

FORMULA

G.f. x*(1+6*x+5*x^2+4*x^3+9*x^4) / ((1-x)*(1+x)*(1-x+x^2)*(1+x+x^2)).

a(n) = a(n-6).

a(n) = 25-a(n-1)-a(n-2)-a(n-3)-a(n-4)-a(n-5).

For n>0, a(n) = A010879(A001109(n)) = A010879(sqrt(A001110(n))) = mod(A001109(n),10).

EXAMPLE

The fourth non-zero square number that is also a triangular number is 204^2. As 204 has units' digit 4, then a(4)=4.

MATHEMATICA

LinearRecurrence[{0, 0, 0, 0, 0, 1}, {1, 6, 5, 4, 9, 0}, 86]

PROG

(PARI) a(n)=[0, 1, 6, 5, 4, 9][n%6+1] \\ Charles R Greathouse IV, Jan 31 2012

CROSSREFS

Cf. A010879, A001109, A001110.

Sequence in context: A200096 A220086 A094773 * A168239 A019131 A019132

Adjacent sequences:  A205648 A205649 A205650 * A205652 A205653 A205654

KEYWORD

nonn,easy

AUTHOR

Ant King, Jan 31 2012

STATUS

approved

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Last modified November 27 16:30 EST 2014. Contains 250240 sequences.