cp's OEIS Frontend

A247907 Expansion of (1 + x) / ((1 - x^4) * (1 - x - x^5)) in powers of x.

%I A247907 #22 Sep 08 2022 08:46:09
%S A247907 1,2,2,2,3,5,7,9,12,16,21,28,38,51,67,88,117,156,207,274,363,481,637,
%T A247907 844,1119,1483,1964,2601,3446,4566,6049,8013,10615,14062,18628,24677,
%U A247907 32691,43307,57369,75997,100675,133367,176674,234043,310041,410717,544084
%N A247907 Expansion of (1 + x) / ((1 - x^4) * (1 - x - x^5)) in powers of x.
%H A247907 Vincenzo Librandi, <a href="/A247907/b247907.txt">Table of n, a(n) for n = 0..1000</a>
%H A247907 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1,1,-1,1,-1).
%F A247907 G.f.: 1 / ((1 - x) * (1 - x + x^2) * (1 + x^2) * (1 - x^2 - x^3)).
%F A247907 a(n) = -A247918(-8-n) for all n in Z.
%F A247907 Convolution of A003520 and A133872.
%F A247907 0 = a(n) + a(n+4) - a(n+5) + mod(floor((n-1) / 2), 2) for all n in Z.
%F A247907 0 = a(n) - a(n+1) + a(n+2) - a(n+3) + a(n+4) - 2*a(n+5) + 2*a(n+6) - 2*a(n+7) + a(n+8) for all n in Z.
%e A247907 G.f. = 1 + 2*x + 2*x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 7*x^6 + 9*x^7 + 12*x^8 + ...
%t A247907 CoefficientList[Series[(1 + x)/((1 - x^4) (1 - x - x^5)), {x, 0, 100}], x] (* _Vincenzo Librandi_, Sep 27 2014 *)
%o A247907 (PARI) {a(n) = if( n<0, n=-8-n; polcoeff( -1 / ((1 - x) * (1 - x + x^2) * (1 + x^2) * (1 + x - x^3)) + x * O(x^n), n), polcoeff( 1 / ((1 - x) * (1 - x + x^2) * (1 + x^2) * (1 - x^2 - x^3)) + x * O(x^n), n))};
%o A247907 (Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 +x)/((1-x^4)*(1-x-x^5))));  // _G. C. Greubel_, Aug 04 2018
%Y A247907 Cf. A003520, A133872, A247918.
%K A247907 nonn,easy
%O A247907 0,2
%A A247907 _Michael Somos_, Sep 26 2014