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

1,3

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

Table of n, a(n) for n=1..30.

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

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

Crossrefs

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

Cf. A010472.

Sequence in context: A159078 A253090 A154226 * A030027 A082201 A357880

Adjacent sequences: A177184 A177185 A177186 * A177188 A177189 A177190

Keyword

nonn,easy,changed

Author

Mark Dols, May 04 2010

Status

approved