cp's OEIS Frontend

A258000 Expansion of 1/(1-x-x^2-x^3-x^4+x^5+x^6+x^7-x^9).

%I A258000 #22 Sep 08 2022 08:46:12
%S A258000 1,1,2,4,8,14,26,48,89,164,302,557,1028,1896,3496,6448,11893,21935,
%T A258000 40455,74613,137613,253807,468108,863354,1592327,2936808,5416499,
%U A258000 9989915,18424893,33981939,62674564,115593785,213195313,393206621,725210344,1337541166
%N A258000 Expansion of 1/(1-x-x^2-x^3-x^4+x^5+x^6+x^7-x^9).
%C A258000 This sequence counts partially ordered partitions of (n) into parts (1,2,3,4) in which only the position (order) of the 1's are important. The 1's behave as placeholders for unordered 2's,3's and 4's.
%H A258000 <a href="/index/Par#partN">Index entries for partition-counting sequences</a>
%H A258000 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,-1,-1,-1,0,1)
%F A258000 a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) - a(n-5) - a(n-6) - a(n-7) + a(n-9)
%F A258000 G.f.: 1/(1-x-x^2-x^3-x^4+x^5+x^6+x^7-x^9).
%e A258000 a(6)=26; these are (42,24=one),(411),(141),(114),(33),(321,231=one),(123,132=one),(312),(213),(3111=four),(222),(2211),(1122),(2112),(1221),(1212),(2121),(21111=five),(111111).
%t A258000 LinearRecurrence[{1, 1, 1, 1, -1, -1, -1, 0, 1}, {1, 1, 2, 4, 8, 14, 26, 48, 89}, 50] (* _Vincenzo Librandi_, May 19 2015 *)
%o A258000 (PARI) Vec(1/(-x^9+x^7+x^6+x^5-x^4-x^3-x^2-x+1) + O(x^100)) \\ _Colin Barker_, May 17 2015
%o A258000 (Magma) I:=[1,1,2,4,8,14,26,48,89]; [n le 9 select I[n] else Self(n-1)+Self(n-2)+Self(n-3)+Self(n-4)-Self(n-5)-Self(n-6)-Self(n-7)+Self(n-9): n in [1..40]]; // _Vincenzo Librandi_, May 19 2015
%K A258000 nonn,easy
%O A258000 0,3
%A A258000 _David Neil McGrath_, May 16 2015
%E A258000 More terms from _Vincenzo Librandi_, May 19 2015