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A133846
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a(n)*a(n-7) = a(n-1)a(n-6)+a(n-3)+a(n-4) with initial terms a(1)=...=a(7)=1.
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6
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1, 1, 1, 1, 1, 1, 1, 3, 5, 7, 11, 19, 31, 111, 195, 283, 465, 831, 1381, 4969, 8741, 12697, 20885, 37353, 62101, 223471, 393121, 571051, 939331, 1680031, 2793151, 10051203, 17681675, 25684567, 42248981, 75564019, 125629681, 452080641, 795282225
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OFFSET
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1,8
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,46,0,0,0,0,0,-46,0,0,0,0,0,1).
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FORMULA
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G.f.: x*(1 +x +x^2 +x^3 +x^4 +x^5 -45*x^6 -43*x^7 -41*x^8 -39*x^9 -35*x^10 -27*x^11 +31*x^12 +19*x^13 +11*x^14 +7*x^15 +5*x^16 +3*x^17) / ((1 -x)*(1 +x)*(1 -x +x^2)*(1 +x +x^2)*(1 -45*x^6 +x^12)). - Colin Barker, Jul 18 2016
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MAPLE
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a := proc(n) option remember; if n<=7 then RETURN(1); else RETURN((a(n-1)*a(n-6)+a(n-3)+a(n-4))/a(n-7)); fi; end;
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MATHEMATICA
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nxt[{a_, b_, c_, d_, e_, f_, g_}]:={b, c, d, e, f, g, (g*b+e+d)/a}; Transpose[ NestList[ nxt, {1, 1, 1, 1, 1, 1, 1}, 40]][[1]] (* or *) LinearRecurrence[ {0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, -46, 0, 0, 0, 0, 0, 1}, {1, 1, 1, 1, 1, 1, 1, 3, 5, 7, 11, 19, 31, 111, 195, 283, 465, 831}, 40] (* Harvey P. Dale, Aug 21 2014 *)
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PROG
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(PARI) a(k=7, n) = {K = (k-1)/2; vds = vector(n); for (i=1, 2*K+1, vds[i] = 1; ); for (i=2*K+2, n, vds[i] = (vds[i-1]*vds[i-2*K]+vds[i-K]+vds[i-K-1])/vds[i-2*K-1]; ); for (i=1, n, print1(vds[i], ", "); ); } \\ Michel Marcus, Nov 01 2012
(PARI) Vec(x*(1 +x +x^2 +x^3 +x^4 +x^5 -45*x^6 -43*x^7 -41*x^8 -39*x^9 -35*x^10 -27*x^11 +31*x^12 +19*x^13 +11*x^14 +7*x^15 +5*x^16 +3*x^17) / ((1 -x)*(1 +x)*(1 -x +x^2)*(1 +x +x^2)*(1 -45*x^6 +x^12)) + O(x^50)) \\ Colin Barker, Jul 18 2016
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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