A205961 Expansion of 1/(-32*x^5 + 8*x^3 - 4*x^2 - x + 1).

1, 1, 5, 1, 13, 9, 85, 177, 477, 921, 1701, 4289, 9389, 28201, 60917, 153041, 308349, 733625, 1645125, 4062177, 9670989, 22625865, 52288405, 118067953, 276204317, 639640537, 1523941861

Offset: 0

Author

Roger L. Bagula, Feb 02 2012

Keywords

• nonn
• easy
• less

Comments

Previous name was: Expand 1/(1 - x/2 - x^2 + x^3 - x^5) in powers of x, then multiply coefficient of x^n by 2^n to get integers.

The sequence is from -1 + x^2 - x^3 - x^4/2 + x^5 with real root 1.1647612555333289.

The limiting ratio of successive terms is 2*1.1647612555333289.

Recurrence: -32 *a (n) + 8 *a (n + 2) - 4 *a (n + 4) + a (n + 5) == 0; with a (1) == 1; a (2) == 1; a (3) == 5; a (4) == 1; a (5) == 13 (from FindSequenceFunction[]).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,4,-8,0,32).

Crossrefs

Cf. A202907, A167602, A167602, A117791, A107293, A204631, A185357.

Programs

Mathematica

CoefficientList[Series[1/(1 - x/2 - x^2 + x^3 - x^5), {x, 0, 50}], x] * 2^Range[0, 50]
LinearRecurrence[{1,4,-8,0,32}, {1,1,5,1,13}, 100] (* G. C. Greubel, Nov 16 2016 *)

PARI

for(n=0,30, print1(2^n*polcoeff(1/(1-x/2 - x^2 + x^3 - x^5) + O(x^32), n), ", ")) \\ G. C. Greubel, Nov 16 2016

Extensions

New name from Joerg Arndt, Nov 19 2016