A282737 Expansion of (x^6 - x^4 + x^3 - x - 1)/((x - 1)^3*(x + 1)^2).

1, 2, 4, 5, 9, 10, 15, 16, 22, 23, 30, 31, 39, 40, 49, 50, 60, 61, 72, 73, 85, 86, 99, 100, 114, 115, 130, 131, 147, 148, 165, 166, 184, 185, 204, 205, 225, 226, 247, 248, 270, 271, 294, 295, 319, 320, 345, 346, 372, 373, 400, 401, 429, 430, 459, 460, 490, 491, 522, 523, 555, 556, 589, 590, 624

Offset: 0

Author

N. J. A. Sloane, Mar 04 2017

Keywords

• nonn
• easy

References

• Mark Thomas, Email to N. J. A. Sloane, Mar 03 2017

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

First differences give A282738.

Programs

PARI

Vec((x^6 - x^4 + x^3 - x - 1)/((x - 1)^3*(x + 1)^2) + O(x^60)) \\ Colin Barker, Mar 04 2017

Formula

From Colin Barker, Mar 04 2017: (Start)

a(n) = (n^2 + 14*n) / 8 for n>1 and even.

a(n) = (n^2 + 12*n - 5) / 8 for n>1 and odd.

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4. (End)