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 A133854 a(n)*a(n-13) = a(n-1)*a(n-12)+a(n-6)+a(n-7) with initial terms a(1)=...=a(13)=1. 6
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 7, 9, 11, 13, 17, 25, 37, 53, 73, 97, 321, 549, 781, 1017, 1257, 1501, 1995, 2985, 4471, 6453, 8931, 11905, 39433, 67457, 95977, 124993, 154505, 184513, 245273, 367041, 549817, 793601, 1098393, 1464193, 4849891 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,14 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..5754 P. Heideman and E. Hogan, A New Family of Somos-Like Recurrences, arXiv:0709.2529 [math.CO], 2007-2009. Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 124, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -124, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1). FORMULA Sequence also generated by the linear recurrence 124*(u(n-12)-u(n-24))+u(n-36) with the initial 36 terms given by the quadratic recurrence. G.f.: x*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6 +x^7 +x^8 +x^9 +x^10 +x^11 -123*x^12 -121*x^13 -119*x^14 -117*x^15 -115*x^16 -113*x^17 -111*x^18 -107*x^19 -99*x^20 -87*x^21 -71*x^22 -51*x^23 +97*x^24 +73*x^25 +53*x^26 +37*x^27 +25*x^28 +17*x^29 +13*x^30 +11*x^31 +9*x^32 +7*x^33 +5*x^34 +3*x^35) / ((1 -x)*(1 +x)*(1 -x +x^2)*(1 +x^2)*(1 +x +x^2)*(1 -x^2 +x^4)*(1 +11*x^6 -x^12)*(1 -11*x^6 -x^12)). - Colin Barker, Jul 18 2016 MAPLE a := proc(n) option remember; if n<=13 then RETURN(1); else RETURN((a(n-1)*a(n-12)+a(n-6)+a(n-7))/a(n-13)); fi; end; MATHEMATICA RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==a[5]==a[6]==a[7]== a[8]== a[9]== a[10]== a[11]== a[12]==a[13]==1, a[n]==(a[n-1]a[n-12]+a[n-6]+ a[n-7])/ a[n-13]}, a, {n, 50}] (* Harvey P. Dale, Nov 24 2015 *) PROG (PARI) a(k=13, 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 +x^6 +x^7 +x^8 +x^9 +x^10 +x^11 -123*x^12 -121*x^13 -119*x^14 -117*x^15 -115*x^16 -113*x^17 -111*x^18 -107*x^19 -99*x^20 -87*x^21 -71*x^22 -51*x^23 +97*x^24 +73*x^25 +53*x^26 +37*x^27 +25*x^28 +17*x^29 +13*x^30 +11*x^31 +9*x^32 +7*x^33 +5*x^34 +3*x^35) / ((1 -x)*(1 +x)*(1 -x +x^2)*(1 +x^2)*(1 +x +x^2)*(1 -x^2 +x^4)*(1 +11*x^6 -x^12)*(1 -11*x^6 -x^12)) + O(x^60)) \\ Colin Barker, Jul 18 2016 CROSSREFS Cf. A072881, A092264, A133846, A133847, A133848. Sequence in context: A062090 A172095 A309361 * A239008 A291343 A030155 Adjacent sequences:  A133851 A133852 A133853 * A133855 A133856 A133857 KEYWORD easy,nonn AUTHOR Emilie Hogan, Sep 26 2007 STATUS approved

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Last modified January 26 17:22 EST 2020. Contains 331280 sequences. (Running on oeis4.)