A247907 - OEIS

%I #22 Sep 08 2022 08:46:09

%S 1,2,2,2,3,5,7,9,12,16,21,28,38,51,67,88,117,156,207,274,363,481,637,

%T 844,1119,1483,1964,2601,3446,4566,6049,8013,10615,14062,18628,24677,

%U 32691,43307,57369,75997,100675,133367,176674,234043,310041,410717,544084

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

%H Vincenzo Librandi, <a href="/A247907/b247907.txt">Table of n, a(n) for n = 0..1000</a>

%H <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 G.f.: 1 / ((1 - x) * (1 - x + x^2) * (1 + x^2) * (1 - x^2 - x^3)).

%F a(n) = -A247918(-8-n) for all n in Z.

%F Convolution of A003520 and A133872.

%F 0 = a(n) + a(n+4) - a(n+5) + mod(floor((n-1) / 2), 2) for all n in Z.

%F 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 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 CoefficientList[Series[(1 + x)/((1 - x^4) (1 - x - x^5)), {x, 0, 100}], x] (* _Vincenzo Librandi_, Sep 27 2014 *)

%o (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 (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 Cf. A003520, A133872, A247918.

%K nonn,easy

%O 0,2

%A _Michael Somos_, Sep 26 2014