A177187 Union of A057080 and A001090.

1, 1, 9, 8, 71, 63, 559, 496, 4401, 3905, 34649, 30744, 272791, 242047, 2147679, 1905632, 16908641, 15003009, 133121449, 118118440, 1048062951, 929944511, 8251382159, 7321437648, 64962994321, 57641556673, 511452572409, 453811015736, 4026657584951, 3572846569215

Offset: 1

Author

Mark Dols, May 04 2010

Keywords

• nonn
• easy

Comments

Column sums of shifted Pascal-like array:

1..1..10..10..100..100.1000.1000

......-1..-2..-30..-40.-500.-600

................1....3...60..100

.........................-1...-4

-------------------------------- +

1..1...9...8...71...63..559..496

Decimal expansion of ratio n/(n+1) is accumulation of Catalan numbers; (5 +/- sqrt(15)).

Links

• Index entries for linear recurrences with constant coefficients, signature (0,8,0,-1).

Crossrefs

Cf. A057080, A001090, A041059, A004189, A000108.

Cf. A010472.

Formula

For n odd a(n) = 10*a(n-1) - a(n-2), for n even a(n) = a(n-1) - a(n-2); with a(0) = 0, a(1) = 1.

G.f.: x*(1+x+x^2) / ( 1-8*x^2+x^4 ). - R. J. Mathar, Nov 11 2011