A167280 Period length 12: 0,0,1,2,4,7,4,8,7,4,8,5 (and repeat).

0, 0, 1, 2, 4, 7, 4, 8, 7, 4, 8, 5, 0, 0, 1, 2, 4, 7, 4, 8, 7, 4, 8, 5, 0, 0, 1, 2, 4, 7, 4, 8, 7, 4, 8, 5, 0, 0, 1, 2, 4, 7, 4, 8, 7, 4, 8, 5, 0, 0, 1, 2, 4, 7, 4, 8, 7, 4, 8, 5, 0, 0, 1, 2, 4, 7, 4, 8, 7, 4, 8, 5, 0, 0, 1, 2, 4, 7, 4, 8, 7, 4, 8, 5, 0, 0, 1, 2, 4, 7, 4, 8, 7, 4, 8, 5, 0, 0, 1, 2, 4, 7, 4, 8, 7

Offset: 0

Author

Paul Curtz, Nov 01 2009

Keywords

• nonn
• easy

Comments

The sum of the terms in the period is 50, so the partial sums of the sequence are also 12-periodic if reduced modulo 50 or modulo 10.

The weighted partial sums b(n) = sum_{i=0..n} a(i)*2^i obey b(n) = b(n+12) (mod 10).

Third column is A000689. (Which table or array is this referring to? R. J. Mathar, Nov 01 2009)

The set of digits in the period is the same as in A141425.

A derived sequence with terms a(n)+a(n+6) has period length 6: 4, 8, 8, 6, 12, 12 (repeat).

Links

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

Formula

a(n) = A113405(n+1) mod 10.

G.f.: x^2*(1+2*x+4*x^2+7*x^3+4*x^4+8*x^5+7*x^6+4*x^7+8*x^8+5*x^9)/( (1-x)*(1+x+x^2)*(1+x)*(1-x+x^2)*(1+x^2)*(x^4-x^2+1)) [R. J. Mathar, Nov 03 2009]

Extensions

Edited by R. J. Mathar, Nov 05 2009