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a(n) = a(n-1) + Sum_{0<k<=n/5} a(n-5k) with a(0)=1.
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%I #9 Mar 12 2017 12:45:07

%S 1,1,1,1,1,2,3,4,5,6,9,13,18,24,31,43,60,83,113,151,206,283,389,532,

%T 721,982,1342,1837,2512,3422,4665,6367,8699,11886,16218,22126,30195,

%U 41226,56299,76849,104883,143147,195404,266776,364175,497092,678503,926164

%N a(n) = a(n-1) + Sum_{0<k<=n/5} a(n-5k) with a(0)=1.

%C If presented in five rows a(5n) a(5n+1).. a(5n+4) each term is the sum of the previous term in the sequence and the partial sum of its row.

%H G. C. Greubel, <a href="/A113444/b113444.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,2,-1).

%F G.f.: (1-x^5)/(1-x-2*x^5+x^6).

%F a(n) = a(n-1) + 2*a(n-5) - a(n-6).

%F a(n) = 11*a(n-5) -45*a(n-10) +90*a(n-15) -90*a(n-20) +37*a(n-25)-a(n-30).

%t CoefficientList[Series[(1 - x^5)/(1 - x - 2*x^5 + x^6), {x,0,50}], x] (* _G. C. Greubel_, Mar 11 2017 *)

%o (PARI) x='x+O('x^50); Vec((1-x^5)/(1-x-2*x^5+x^6)) \\ _G. C. Greubel_, Mar 11 2017

%Y Cf. A113435, A113439, A028495.

%K nonn,easy

%O 0,6

%A _Floor van Lamoen_, Nov 04 2005