A147598 -id:A147598 - cp's OEIS frontend

A147593 Expansion of 1/(1 - x + x^3 - 3*x^4 + x^5 - x^7 + x^8).

1, 1, 1, 0, 2, 3, 5, 3, 6, 8, 16, 16, 24, 28, 50, 61, 91, 109, 170, 220, 327, 415, 607, 800, 1164, 1536, 2192, 2928, 4172, 5616, 7921, 10705, 15049, 20460, 28638, 39027, 54453, 74451, 103662, 141996, 197288, 270704, 375632, 516096, 715258, 983661, 1362091

Offset: 0

Roger L. Bagula, Nov 08 2008

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,-1,3,-1,0,1,-1).

Cf. A147598, A147605, A147606, A147607, A147617, A147620.

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/((1+x^3-x^4)*(1-x-x^4)) )); // G. C. Greubel, Oct 25 2022

f[x_]= x^4-x^3-1; CoefficientList[Series[-1/(x^4*f[x]*f[1/x]), {x,0,50}], x]

def A147593_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/((1+x^3-x^4)*(1-x-x^4)) ).list()
A147593_list(50) # G. C. Greubel, Oct 25 2022

G.f.: -1/(x^4*f(x)*f(1/x)), where f(x) = -1 - x^3 + x^4.

G.f.: 1/((1+x^3-x^4)*(1-x-x^4)). - Colin Barker, Nov 04 2012

Edited by Joerg Arndt and Colin Barker, Nov 04 2012.

A147592 Expansion of 1/(1 + x - x^2 - 3*x^3 - x^4 + x^5 + x^6).

Original entry on oeis.org

1, -1, 2, 0, 0, 4, -2, 5, 3, 0, 12, 0, 12, 16, 5, 35, 18, 36, 64, 40, 110, 105, 135, 240, 216, 384, 472, 560, 905, 999, 1458, 1960, 2368, 3500, 4302, 5805, 7947, 9936, 13860, 17920, 23588, 32096, 41229, 55755, 73570, 96460, 129920, 169680, 226206, 300369

Offset: 0

Roger L. Bagula, Nov 08 2008

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-1,1,3,1,-1,-1).

Cf. A147593, A147598, A147605, A147606.

R:=PowerSeriesRing(Integers(), 60); Coefficients(R!( 1/((1+x-x^3)*(1-x^2-x^3)) )); // G. C. Greubel, Oct 25 2022

f[x_]= x^3-x-1; CoefficientList[Series[-1/(x^3*f[x]*f[1/x]), {x,0,60}], x]
LinearRecurrence[{-1,1,3,1,-1,-1},{1,-1,2,0,0,4},60] (* Harvey P. Dale, Sep 23 2020 *)

def A147592_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/((1+x-x^3)*(1-x^2-x^3)) ).list()
A147592_list(60) # G. C. Greubel, Oct 25 2022

G.f.: -1/(x^3*f(x)*f(1/x)), where f(x) = -1 - x + x^3.

G.f.: 1/((1+x-x^3)*(1-x^2-x^3)). - Colin Barker, Nov 04 2012

Edited by Joerg Arndt and Colin Barker, Nov 04 2012

cp's OEIS Frontend

A147593 Expansion of 1/(1 - x + x^3 - 3*x^4 + x^5 - x^7 + x^8).

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