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%I A218470 #31 Sep 08 2022 08:46:04
%S A218470 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 A218470 36,39,42,45,48,51,54,58,62,66,70,74,78,82,86,90,95,100,105,110,115,
%U A218470 120,125,130,135,141,147,153,159,165,171,177,183,189,196,203,210,217,224
%N A218470 Partial sums of floor(n/9).
%C A218470 Apart from the initial zeros, the same as A008727.
%H A218470 G. C. Greubel, <a href="/load/view.php?a=aHR0cDovL29laXMub3JnL0EyMTg0NzAvYjIxODQ3MC50eHQ">Table of n, a(n) for n = 0..1000</a>
%H A218470 <a href="/load/view.php?a=aHR0cDovL29laXMub3JnL2luZGV4L1JlYyNvcmRlcl8xMQ">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,1,-2,1).
%F A218470 a(9n)   = A051682(n).
%F A218470 a(9n+1) = A062708(n).
%F A218470 a(9n+2) = A062741(n).
%F A218470 a(9n+3) = A022266(n).
%F A218470 a(9n+4) = A022267(n).
%F A218470 a(9n+5) = A081266(n).
%F A218470 a(9n+6) = A062725(n).
%F A218470 a(9n+7) = A062728(n).
%F A218470 a(9n+8) = A027468(n).
%F A218470 G.f.: x^9/((1-x)^2*(1-x^9)). - _Bruno Berselli_, Mar 27 2013
%e A218470 As square array:
%e A218470 ..0....0....0....0....0....0....0....0....0....
%e A218470 ..1....2....3....4....5....6....7....8....9....
%e A218470 .11...13...15...17...19...21...23...25...27....
%e A218470 .30...33...36...39...42...45...48...51...54....
%e A218470 .58...62...66...70...74...78...82...86...90....
%e A218470 .95..100..105..110..115..120..125..130..135....
%e A218470 141..147..153..159..165..171..177..183..189....
%e A218470 196..203..210..217..224..231..238..245..252....
%e A218470 ...
%t A218470 Accumulate[Floor[Range[0, 100]/9]] (* _Jean-François Alcover_, Mar 27 2013 *)
%o A218470 (Magma) [&+[Floor(k/9): k in [0..n]]: n in [0..70]]; // _Bruno Berselli_, Mar 27 2013
%o A218470 (PARI) for(n=0,50, print1(sum(k=0,n, floor(k/9)), ", ")) \\ _G. C. Greubel_, Dec 13 2016
%o A218470 (PARI) a(n)=my(k=n\9); k*(9*k-7)/2 + k*(n-9*k) \\ _Charles R Greathouse IV_, Dec 13 2016
%Y A218470 Cf. similar sequences: A118729, A174109, A174738.
%K A218470 nonn,tabf,easy
%O A218470 0,11
%A A218470 _Philippe Deléham_, Mar 26 2013

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