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Partial sums of floor(n/9).
16

%I #31 Sep 08 2022 08:46:04

%S 0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,11,13,15,17,19,21,23,25,27,30,33,

%T 36,39,42,45,48,51,54,58,62,66,70,74,78,82,86,90,95,100,105,110,115,

%U 120,125,130,135,141,147,153,159,165,171,177,183,189,196,203,210,217,224

%N Partial sums of floor(n/9).

%C Apart from the initial zeros, the same as A008727.

%H G. C. Greubel, <a href="/A218470/b218470.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,1,-2,1).

%F a(9n) = A051682(n).

%F a(9n+1) = A062708(n).

%F a(9n+2) = A062741(n).

%F a(9n+3) = A022266(n).

%F a(9n+4) = A022267(n).

%F a(9n+5) = A081266(n).

%F a(9n+6) = A062725(n).

%F a(9n+7) = A062728(n).

%F a(9n+8) = A027468(n).

%F G.f.: x^9/((1-x)^2*(1-x^9)). - _Bruno Berselli_, Mar 27 2013

%e As square array:

%e ..0....0....0....0....0....0....0....0....0....

%e ..1....2....3....4....5....6....7....8....9....

%e .11...13...15...17...19...21...23...25...27....

%e .30...33...36...39...42...45...48...51...54....

%e .58...62...66...70...74...78...82...86...90....

%e .95..100..105..110..115..120..125..130..135....

%e 141..147..153..159..165..171..177..183..189....

%e 196..203..210..217..224..231..238..245..252....

%e ...

%t Accumulate[Floor[Range[0, 100]/9]] (* _Jean-François Alcover_, Mar 27 2013 *)

%o (Magma) [&+[Floor(k/9): k in [0..n]]: n in [0..70]]; // _Bruno Berselli_, Mar 27 2013

%o (PARI) for(n=0,50, print1(sum(k=0,n, floor(k/9)), ", ")) \\ _G. C. Greubel_, Dec 13 2016

%o (PARI) a(n)=my(k=n\9); k*(9*k-7)/2 + k*(n-9*k) \\ _Charles R Greathouse IV_, Dec 13 2016

%Y Cf. similar sequences: A118729, A174109, A174738.

%K nonn,tabf,easy

%O 0,11

%A _Philippe Deléham_, Mar 26 2013