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Modified quadranacci series.
1

%I #13 Jul 07 2016 01:08:49

%S 0,1,1,1,1,2,2,2,3,4,4,6,7,8,12,14,15,23,27,29,44,52,56,85,100,108,

%T 164,193,208,316,372,401,609,717,773,1174,1382,1490,2263,2664,2872,

%U 4362,5135,5536,8408,9898,10671,16207,19079,20569,31240,36776,39648,60217,70888,76424,116072,136641

%N Modified quadranacci series.

%H G. C. Greubel, <a href="/A274759/b274759.txt">Table of n, a(n) for n = 0..1000</a>

%H Ian Bruce, <a href="http://www.fq.math.ca/Scanned/22-3/bruce.pdf">A Modified Tribonacci Sequence</a>, The Fibonacci Quarterly 22, no.3 (1984):244-246

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,0,0,1,0,0,1,0,0,1).

%F a(3n) = a(3n-3) + a(3n-6) + a(3n-9) + a(3n-12).

%F a(3n + 2) = a(3n + 1) + a(3n - 2).

%F a(3n + 3) = a(3n + 1) + a(3n - 1).

%F a(3n + 4) = a(3n + 1) + a(3n).

%F G.f.: x*(1 + x + x^2 + x^4 + x^5 + x^8)/(1 - x^3 - x^6 - x^9 - x^12).

%t CoefficientList[Series[x*(1 + x + x^2 + x^4 + x^5 + x^8)/(1 - x^3 - x^6 - x^9 - x^12), {x, 0, 25}], x] (* or *) LinearRecurrence[{0,0,1,0,0,1,0,0, 1,0,0,1},{0,1,1,1,1,2,2,2,3,4,4,6}, 50]

%o (PARI) concat(0, Vec(x*(1+x+x^2+x^4+x^5+x^8)/(1-x^3-x^6-x^9-x^12) + O(x^99))) \\ _Altug Alkan_, Jul 04 2016

%Y Cf. A213816.

%K nonn

%O 0,6

%A _G. C. Greubel_, Jul 04 2016