cp's OEIS Frontend

A175782 Expansion of 1/(1 - x - x^20 - x^39 + x^40).

%I A175782 #32 Jun 30 2023 18:02:42
%S A175782 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,10,11,12,13,
%T A175782 14,15,16,17,18,19,20,22,24,27,31,36,42,49,57,66,76,87,99,112,126,141,
%U A175782 157,174,192,211,231,254,279,307,339,376,419,469,527,594
%N A175782 Expansion of 1/(1 - x - x^20 - x^39 + x^40).
%C A175782 Limiting ratio of a(n)/a(n-1) = 1.119189829034646... .
%C A175782 A quasi - Salem polynomial based on the symmetrical polynomial defined by p(x,0) = 1, p(x,n) = x^(2*n) - x^(2*n - 1) - x^n - x + 1 for n>=1.
%C A175782 The polynomial has one real and two complex roots outside the unit circle.
%H A175782 Alois P. Heinz, <a href="/A175782/b175782.txt">Table of n, a(n) for n = 0..1000</a>
%H A175782 <a href="/index/Rec#order_40">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
%F A175782 a(n) = a(n-1) + a(n-20) + a(n-39) - a(n-40). - _Franck Maminirina Ramaharo_, Oct 31 2018
%p A175782 gf:= 1/(1-x-x^20-x^39+x^40):
%p A175782 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A175782 seq(a(n), n=0..100);  # _Alois P. Heinz_, Jul 27 2012
%t A175782 CoefficientList[Series[1/(1 - x - x^20 - x^39 + x^40), {x, 0, 50}], x]
%t A175782 LinearRecurrence[{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1},{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22},70] (* _Harvey P. Dale_, Jun 30 2023 *)
%o A175782 (PARI) Vec(O(x^99)+1/(1 - x - x^20 - x^39 + x^40)) \\ N.B.: This yields a vector whose first component v[1] equals a(0), i.e., the offset is shifted by one. - _M. F. Hasler_, Dec 11 2010
%o A175782 (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x-x^20-x^39+x^40))); // _G. C. Greubel_, Nov 03 2018
%Y A175782 Cf. A175739.
%Y A175782 Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A181600, A204631, A225391, A225393, A225394, A225482, A225499.
%K A175782 nonn,easy
%O A175782 0,21
%A A175782 _Roger L. Bagula_, Dec 04 2010