A304490 a(1) = a(2) = a(3) = 1, a(4) = 5, a(5) = 6, a(6) = 4; a(n) = a(n-a(n-2)) + a(n-a(n-4)) for n > 6.
1, 1, 1, 5, 6, 4, 5, 6, 6, 9, 10, 5, 6, 12, 12, 15, 16, 5, 6, 18, 18, 21, 22, 5, 6, 24, 24, 27, 28, 5, 6, 30, 30, 33, 34, 5, 6, 36, 36, 39, 40, 5, 6, 42, 42, 45, 46, 5, 6, 48, 48, 51, 52, 5, 6, 54, 54, 57, 58, 5, 6, 60, 60, 63, 64, 5, 6, 66, 66, 69, 70, 5, 6, 72, 72, 75, 76, 5, 6, 78, 78, 81, 82, 5, 6
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (2, -3, 4, -5, 6, -5, 4, -3, 2, -1).
Programs
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PARI
q=vector(85); q[1]=1;q[2]=1;q[3]=1;q[4]=5;q[5]=6;q[6]=4; for(n=7, #q, q[n] = q[n-q[n-2]]+q[n-q[n-4]]); q
Formula
a(6*k) = 5, a(6*k+1) = 6, a(6*k+2) = a(6*k+3) = 6*k, a(6*k+4) = 6*k+3, a(6*k+5) = 6*k+4 for k > 1.
Conjectures from Colin Barker, May 14 2018: (Start)
G.f.: x*(1 - x + 2*x^2 + 2*x^3 + 2*x^5 - x^6 + 4*x^7 - 3*x^8 + x^9 - x^10 - 2*x^11 + 2*x^12 - x^13 + x^14 + x^15 - x^16) / ((1 - x)^2*(1 - x + x^2)^2*(1 + x + x^2)^2).
a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5) - 5*a(n-6) + 4*a(n-7) - 3*a(n-8) + 2*a(n-9) - a(n-10) for n>17.
(End)
Comments