A078050 Expansion of (1-x)/(1+x+2*x^2).

1, -2, 0, 4, -4, -4, 12, -4, -20, 28, 12, -68, 44, 92, -180, -4, 364, -356, -372, 1084, -340, -1828, 2508, 1148, -6164, 3868, 8460, -16196, -724, 33116, -31668, -34564, 97900, -28772, -167028, 224572, 109484, -558628, 339660, 777596, -1456916, -98276, 3012108, -2815556, -3208660, 8839772

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Comments

INVERTi transform of A005408, (2n + 1) = A078050 signed: (1, 2, 0, -4, -4, 4, 12, 4, -20, -28, ...) = left border of triangle A144106. - Gary W. Adamson, Sep 11 2008

Links

• Index entries for linear recurrences with constant coefficients, signature (-1,-2).

Crossrefs

Cf. A005408, A144106. - Gary W. Adamson, Sep 11 2008

Cf. A208904.

Programs

PARI

Vec((1-x)/(1+x+2*x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012

Formula

a(n-1) = Sum_{k=1..n} (-1)^(n-k) * Sum_{i=0..n} binomial(k,n-i) * binomial(k+i-1, 2*k-1). - Vladimir Kruchinin, Mar 11 2013

a(n) = A001607(n+1)-A001607(n). - R. J. Mathar, Mar 19 2025