|
%I #69 May 24 2019 11:19:05
%S 4,5,6,7,8,9,11,13,15,17,20,24,28,32,37,44,52,60,69,81,96,112,129,150,
%T 177,208,241,279,327,385,449,520,606,712,834,969,1126,1318,1546,1803,
%U 2095,2444,2864,3349,3898,4539,5308,6213,7247,8437,9847,11521,13460,15684
%N a(n) = sum of a(n-4) and a(n-5), with the lowest possible initial values that will generate a sequence where a(n) is always > a(n-1): 4, 5, 6, 7 and 8.
%C A sum of prior terms in the sequence, like the Fibonacci and Padovan sequences.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,1).
%F a(n) = a(n-4) + a(n-5) with a(1) = 4, a(2) = 5, a(3) = 6, a(4) = 7 and a(5) = 8.
%F G.f.: x*(4 + 5*x + 6*x^2 + 7*x^3 + 4*x^4)/(1 - x^4 - x^5). - _Andrew Howroyd_, Oct 31 2018
%e a(6) = a(6-4) + a(6-5) = a(2) + a(1) = 5 + 4 = 9.
%t Rest@ CoefficientList[Series[x (4 + 5 x + 6 x^2 + 7 x^3 + 4 x^4)/(1 - x^4 - x^5), {x, 0, 54}], x] (* _Michael De Vlieger_, Oct 31 2018 *)
%o (PARI) a(n) = if(n<=5, n+3, a(n-4) + a(n-5)); \\ _Michel Marcus_, Oct 31 2018
%o (PARI) Vec((4 + 5*x + 6*x^2 + 7*x^3 + 4*x^4)/(1 - x^4 - x^5) + O(x^50)) \\ _Andrew Howroyd_, Oct 31 2018
%Y Cf. A000045, A000931, A079398, A164317, A103372, A103373
%K nonn,easy
%O 1,1
%A _Mathew Munro_, Oct 30 2018
%E a(19), a(20) corrected by _Georg Fischer_, May 24 2019
|
