|
%I #15 Sep 08 2022 08:46:18
%S 1,1,1,2,3,5,7,10,16,24,36,54,81,123,185,278,419,631,951,1432,2156,
%T 3248,4892,7368,11097,16713,25173,37914,57103,86005,129535,195098,
%U 293844,442568,666568,1003942,1512073,2277387,3430053,5166126,7780887,11719071,17650511
%N a(n) = a(n-1) + a(n-3) + a(n-5) - a(n-6), a(0) = a(1) = a(2) = 1, a(3) = 2, a(4) = 3, a(5) = 5.
%C If the recursion of A276532 is used to define b(n) = (b(n-1) * b(n-6) + b(n-2) * b(n-3) * b(n-4) * b(n-5)) / b(n-7), with b(0), ..., b(6) variables, then the denominator of b(n) = Product_{k=0..6} b(k)^a(n-k-7) if n>=8.
%H Seiichi Manyama, <a href="/A278706/b278706.txt">Table of n, a(n) for n = 0..5623</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 1, 0, 1, -1).
%F G.f.: 1 / (1 - x - x^3 - x^5 + x^6).
%F 0 = a(n) - a(n-1) - a(n-3) - a(n-5) + a(n-6) for all n in Z.
%F a(n) = - a(-6-n) for all n in Z.
%e G.f. = 1 + x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 7*x^6 + 10*x^7 + 16*x^8 + ...
%t LinearRecurrence[{1, 0, 1, 0, 1, -1}, {1, 1, 1, 2, 3, 5}, 45] (* _Vincenzo Librandi_, Nov 27 2016 *)
%o (PARI) {a(n) = my(m=n, s=1); if( n<0, m=-6-n; s=-1); s * polcoeff( 1 / (1 - x - x^3 - x^5 + x^6) + x * O(x^m), m)};
%o (Magma) I:=[1,1,1,2,3,5]; [n le 6 select I[n] else Self(n-1)+Self(n-3)+Self(n-5)-Self(n-6): n in [1..45]]; // _Vincenzo Librandi_, Nov 27 2016
%Y Cf. A276532.
%K nonn
%O 0,4
%A _Michael Somos_, Nov 26 2016
|
