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FORMULA
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G.f.: F(x) = (1 + 29*x - 330*x^2 - 1870*x^3 + 28792*x^4 - 28880*x^5 - 658872*x^6 + 1808035*x^7 + 7251417*x^8 - 30049286*x^9 - 53844318*x^10 + 331611771*x^11 + 172019006*x^12 - 2314667923*x^13 - 44340353*x^14 + 12301024850*x^15 - 283356562*x^16 - 53520778564*x^17 + 21918429228*x^18 + 188280737400*x^19 - 99256863420*x^20 - 537933519143*x^21 + 304479953092*x^22 + 1292735746371*x^23 - 685767992532*x^24 - 2703731985407*x^25 + 1220124121648*x^26 + 4969059486596*x^27 - 1817137951816*x^28 - 7940770334300*x^29 + 2310666239334*x^30 + 10897173663437*x^31 - 242841325861*x^32 - 12794627581139*x^33 + 1919519246791*x^34 + 12918502357203*x^35 - 852890650171*x^36 -11317650709986*x^37 - 313858871781*x^38 + 8665013739391*x^39 + 1068808054156*x^40 - 5804674396693*x^41 - 1231795216164*x^42 + 3382179875958*x^43 + 984955686298*x^44 - 1694171598050*x^45 - 619939090864*x^46 + 718589694092*x^47 + 323730198889*x^48 - 253619875999*x^49 - 144187648137*x^50 + 72968474423*x^51 + 55421646471*x^52 - 16658211415*x^53 - 18346712946*x^54 + 2894246774*x^55 + 5160729532*x^56 - 351795527*x^57 - 1206372119*x^58 + 22006791*x^59 + 227332930*x^60 + 1758161*x^61 - 33060926*x^62 - 881244*x^63 + 3436739*x^64 + 218431*x^65 - 208580*x^66 - 43625*x^67 - 299*x^68 + 6491*x^69 + 1284*x^70 - 646*x^71 - 104*x^72 + 38*x^73 +3*x^74 -x^75) / ((1-x)^7 * (1-x-x^2)^6 * (1-2*x-x^2+x^3)^5 * (1-2*x-3*x^2+x^3+x^4)^4 * (1-3*x-3*x^2+4*x^3+x^4-x^5)^3 * (1-3*x-6*x^2+4*x^3+5*x^4-x^5-x^6)^2 * (1-4*x-6*x^2+10*x^3+5*x^4-6*x^5-x^6+x^7)).
CONJECTURE 1. a(n) = M_{n,6} = M_{6,n}, where M = A205497.
CONJECTURE 2. Let w=2*cos(Pi/15). Then lim_{n -> infinity) a(n+1)/a(n) = w^6-5*w^4+6*w^2-1 = spectral radius of the 7 X 7 unit-primitive matrix (see [Jeffery]) A_{15,6} = [0,0,0,0,0,0,1; 0,0,0,0,0,1,1; 0,0,0,0,1,1,1; 0,0,0,1,1,1,1; 0,0,1,1,1,1,1; 0,1,1,1,1,1,1; 1,1,1,1,1,1,1].
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