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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: A050150 A062090 A172095 * 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 October 19 13:38 EDT 2018. Contains 316361 sequences. (Running on oeis4.)