A174959 G.f.: x^3*(2*x-1) / ((1-x)*(1-x-x^2)*(1-2*x^2)).

0, 0, 0, -1, 0, -2, 1, -2, 6, 3, 24, 26, 81, 106, 250, 355, 732, 1086, 2073, 3158, 5742, 8899, 15664, 24562, 42273, 66834, 113202, 180035, 301428, 481462, 799273, 1280734, 2112774, 3393507, 5571816, 8965322, 14668209, 23633530, 38563882, 62197411, 101285580

Offset

0,6

References

Burton, David M., Elementary number theory, McGraw Hill, N.Y., 2002, p. 286

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,2,-5,0,2).

Formula

a(n) = Sum_{j=0..floor((n-1)/2)} (-2^j + binomial(n-j-1, j)).

a(n) = Fibonacci(n+1) - 2^ceiling(n/2) - 1.

a(n) = A000045(n+1) - A016116(n+1) - 1.

a(n) = 2*a(n-1) + 2*a(n-2) - 5*a(n-3) + 2*a(n-5) for n^5. - Colin Barker, Dec 01 2019

Mathematica

Table[Sum[-2^(j) +
    Binomial[n - j - 1, j], {j, 0, Floor[(n - 1)/2]}], {n, 0, 30}]

Prog

(PARI) concat([0, 0, 0], -Vec(x^3*(1 - 2*x) / ((1 - x)*(1 - x - x^2)*(1 - 2*x^2)) + O(x^40))) \\ Colin Barker, Dec 01 2019

Crossrefs

Sequence in context: A269223 A121341 A241737 * A126093 A065279 A343383

Adjacent sequences: A174956 A174957 A174958 * A174960 A174961 A174962

Keyword

sign,easy

Author

Roger L. Bagula, Dec 02 2010

Extensions

More terms from Colin Barker, Dec 01 2019

Status

approved