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A130875 Absolute difference of final digits of two consecutive cubes. 0
1, 7, 1, 3, 1, 1, 3, 1, 7, 9, 1, 7, 1, 3, 1, 1, 3, 1, 7, 9, 1, 7, 1, 3, 1, 1, 3, 1, 7, 9, 1, 7, 1, 3, 1, 1, 3, 1, 7, 9, 1, 7, 1, 3, 1, 1, 3, 1, 7, 9, 1, 7, 1, 3, 1, 1, 3, 1, 7, 9, 1, 7, 1, 3, 1, 1, 3, 1, 7, 9, 1, 7, 1, 3, 1, 1, 3, 1, 7, 9, 1, 7, 1, 3, 1, 1, 3, 1, 7, 9, 1, 7, 1, 3, 1, 1, 3, 1, 7, 9, 1, 7, 1, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Periodic with period 10.

LINKS

Table of n, a(n) for n=1..105.

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

FORMULA

a(n)=(1/225)*{197*(n mod 10)-28*[(n+1) mod 10]-118*[(n+2) mod 10]+62*[(n+3) mod 10]-28*[(n+4) mod 10]+17*[(n+5) mod 10]+62*[(n+6) mod 10]-28*[(n+7) mod 10]+152*[(n+8) mod 10]-118*[(n+9) mod 10]}, with n>=0. - Paolo P. Lava, Aug 01 2007

a(n) = 17/5 + (2/5 + 4/5*5^(1/2))*cos(Pi*n/5) + ( - 1/5*((5 - 5^(1/2))^(1/2) + (5 + 5^(1/2))^(1/2))*2^(1/2))*sin(Pi*n/5) + ( - 6/5 + 2/5*5^(1/2))*cos(2*Pi*n/5) + ( - 2/5*2^(1/2)*(5 - 5^(1/2))^(1/2))*sin(2*Pi*n/5) + (2/5 - 4/5*5^(1/2))*cos(3*Pi*n/5) + (1/5*((5 - 5^(1/2))^(1/2) - (5 + 5^(1/2))^(1/2))*2^(1/2))*sin(3*Pi*n/5) + ( - 6/5 - 2/5*5^(1/2))*cos(4*Pi*n/5) + (2/5*2^(1/2)*(5 + 5^(1/2))^(1/2))*sin(4*Pi*n/5) - 4/5*( - 1)^n. - Richard Choulet, Dec 13 2008

a(n) = a(n-10). - Colin Barker, Dec 04 2014

G.f.: -x*(9*x^9+7*x^8+x^7+3*x^6+x^5+x^4+3*x^3+x^2+7*x+1) / ((x-1)*(x+1)*(x^4-x^3+x^2-x+1)*(x^4+x^3+x^2+x+1)). - Colin Barker, Dec 04 2014

MATHEMATICA

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 7, 1, 3, 1, 1, 3, 1, 7, 9}, 105] (* Ray Chandler, Aug 26 2015 *)

Abs[Differences[Mod[#, 10]]]&/@Partition[Range[0, 120]^3, 2, 1]//Flatten (* or *) PadRight[{}, 120, {1, 7, 1, 3, 1, 1, 3, 1, 7, 9}] (* Harvey P. Dale, Oct 27 2019 *)

PROG

(PARI) Vec(-x*(9*x^9+7*x^8+x^7+3*x^6+x^5+x^4+3*x^3+x^2+7*x+1)/((x-1)*(x+1)*(x^4-x^3+x^2-x+1)*(x^4+x^3+x^2+x+1)) + O(x^100)) \\ Colin Barker, Dec 04 2014

CROSSREFS

Cf. A008960.

Sequence in context: A266985 A286912 A239807 * A200923 A317830 A317938

Adjacent sequences:  A130872 A130873 A130874 * A130876 A130877 A130878

KEYWORD

base,easy,nonn

AUTHOR

Giovanni Teofilatto, Jul 25 2007

STATUS

approved

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)