A275173 a(n) = (a(n-3) + a(n-1) * a(n-5)) / a(n-6), a(0) = a(1) = ... = a(5) = 1.
1, 1, 1, 1, 1, 1, 2, 3, 4, 6, 9, 22, 36, 51, 82, 129, 321, 529, 753, 1217, 1921, 4786, 7891, 11236, 18166, 28681, 71462, 117828, 167779, 271266, 428289, 1067137, 1759521, 2505441, 4050817, 6395649, 15935586, 26274979, 37413828, 60490982, 95506441, 237966646
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,16,0,0,0,0,-16,0,0,0,0,1).
Programs
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Mathematica
RecurrenceTable[{a[n] == (a[n - 3] + a[n - 1] a[n - 5])/a[n - 6], a[1] == 1, a[2] == 1, a[3] == 1, a[4] == 1, a[5] == 1, a[6] == 1}, a, {n, 42}] (* or *) CoefficientList[Series[(1 + x + x^2 + x^3 + x^4 - 15 x^5 - 14 x^6 - 13 x^7 - 12 x^8 - 10 x^9 + 9 x^10 + 6 x^11 + 4 x^12 + 3 x^13 + 2 x^14)/((1 - x) (1 + x + x^2 + x^3 + x^4) (1 - 15 x^5 + x^10)), {x, 0, 41}], x] (* Michael De Vlieger, Jul 19 2016 *) nxt[{a_,b_,c_,d_,e_,f_}]:={b,c,d,e,f,(d+f*b)/a}; NestList[nxt,{1,1,1,1,1,1},50][[;;,1]] (* Harvey P. Dale, Jan 06 2024 *) -
PARI
Vec((1 +x +x^2 +x^3 +x^4 -15*x^5 -14*x^6 -13*x^7 -12*x^8 -10*x^9 +9*x^10 +6*x^11 +4*x^12 +3*x^13 +2*x^14) / ((1 -x)*(1 +x +x^2 +x^3 +x^4)*(1 -15*x^5 +x^10)) + O(x^50)) \\ Colin Barker, Jul 19 2016
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Ruby
def A(k, l, n) a = Array.new(k * 2, 1) ary = [1] while ary.size < n + 1 break if (a[1] * a[-1] + a[k] * l) % a[0] > 0 a = *a[1..-1], (a[1] * a[-1] + a[k] * l) / a[0] ary << a[0] end ary end def A275173(n) A(3, 1, n) end
Formula
G.f.: (1 +x +x^2 +x^3 +x^4 -15*x^5 -14*x^6 -13*x^7 -12*x^8 -10*x^9 +9*x^10 +6*x^11 +4*x^12 +3*x^13 +2*x^14) / ((1 -x)*(1 +x +x^2 +x^3 +x^4)*(1 -15*x^5 +x^10)). - Colin Barker, Jul 19 2016
a(n) = 16*a(n-5) - 16*a(n-10) + a(n-15). - G. C. Greubel, Jul 20 2016
Comments