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 A269445 a(n) = Sum_{k=0..n} floor(k/13). 0

%I

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,17,19,21,

%T 23,25,27,29,31,33,35,37,39,42,45,48,51,54,57,60,63,66,69,72,75,78,82,

%U 86,90,94,98,102,106,110,114,118,122,126,130,135,140,145,150,155,160,165,170,175

%N a(n) = Sum_{k=0..n} floor(k/13).

%C Partial sums of A090620.

%C More generally, the ordinary generating function for the Sum_{k=0..n} floor(k/m) is x^m/((1 - x^m)*(1 - x)^2).

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,0,0,0,0,1,-2,1).

%F G.f.: x^13/((1 - x^13)*(1 - x)^2).

%F a(n) = 2*a(n-1) - a(n-2) + a(n-13) - 2*a(n-14) + a(n-15).

%t Table[Sum[Floor[k/13], {k, 0, n}], {n, 0, 73}]

%t LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2}, 74]

%Y Cf. A090620.

%Y Cf. similar sequences of Sum_{k=0..n} floor(k/m): A002620 (m=2), A130518 (m=3), A130519 (m=4), A130520 (m=5), A174709 (m=6), A174738 (m=7), A118729 (m=8), A218470 (m=9), A131242 (m=10), A218530 (m=11), A221912 (m=12), this sequence (m=13).

%K nonn,easy

%O 0,15

%A _Ilya Gutkovskiy_, Feb 27 2016

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Last modified January 18 21:54 EST 2019. Contains 319282 sequences. (Running on oeis4.)