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 A131242 Partial sums of A059995: a(n) = sum_{k=0..n} floor(k/10). 18

%I

%S 0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,10,12,14,16,18,20,22,24,26,28,

%T 30,33,36,39,42,45,48,51,54,57,60,64,68,72,76,80,84,88,92,96,100,105,

%U 110,115,120,125,130,135,140,145,150,156,162,168,174,180,186,192,198

%N Partial sums of A059995: a(n) = sum_{k=0..n} floor(k/10).

%C Complementary with A130488 regarding triangular numbers, in that A130488(n)+10*a(n)=n(n+1)/2=A000217(n).

%H G. C. Greubel, <a href="/A131242/b131242.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,0,1,-2,1).

%F a(n) = (1/2)*floor(n/10)*(2n-8-10*floor(n/10)).

%F a(n) = A059995(n)*(2n-8-10*A059995(n))/2.

%F a(n) = (1/2)*A059995(n)*(n-8+A010879(n)).

%F a(n) = (n-A010879(n))*(n+A010879(n)-8)/20.

%F G.f.: x^10/((1-x^10)(1-x)^2).

%F From _Philippe Deléham_, Mar 27 2013: (Start)

%F a(10n) = A051624(n).

%F a(10n+1) = A135706(n).

%F a(10n+2) = A147874(n+1).

%F a(10n+3) = 2*A005476(n).

%F a(10n+4) = A033429(n).

%F a(10n+5) = A202803(n).

%F a(10n+6) = A168668(n).

%F a(10n+7) = 2*A147875(n).

%F a(10n+8) = A135705(n).

%F a(10n+9) = A124080(n). (End)

%F a(n) = A008728(n-10) for n>= 10. - _Georg Fischer_, Nov 03 2018

%e As square array :

%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

%e 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

%e 12, 14, 16, 18, 20, 22, 24, 26, 28, 30

%e 33, 36, 39, 42, 45, 48, 51, 54, 57, 60

%e 64, 68, 72, 76, 80, 84, 88, 92, 96, 100

%e 105, 110, 115, 120, 125, 130, 135, 140, 145, 150

%e 156, 162, 168, 174, 180, 186, 192, 198, 204, 210

%e ... - _Philippe Deléham_, Mar 27 2013

%t Table[(1/2)*Floor[n/10]*(2*n - 8 - 10*Floor[n/10]), {n,0,50}] (* _G. C. Greubel_, Dec 13 2016 *)

%t Accumulate[Table[FromDigits[Most[IntegerDigits[n]]],{n,0,110}]] (* or *) LinearRecurrence[{2,-1,0,0,0,0,0,0,0,1,-2,1},{0,0,0,0,0,0,0,0,0,0,1,2},120] (* _Harvey P. Dale_, Apr 06 2017 *)

%o (PARI) for(n=0,50, print1((1/2)*floor(n/10)*(2n-8-10*floor(n/10)), ", ")) \\ _G. C. Greubel_, Dec 13 2016

%o (PARI) a(n)=my(k=n\10); k*(n-5*k-4) \\ _Charles R Greathouse IV_, Dec 13 2016

%Y Cf. A008728, A059995, A010879, A002266, A130488, A000217, A002620, A130518, A130519, A130520, A174709, A174738, A118729, A218470.

%K nonn,easy

%O 0,12

%A _Hieronymus Fischer_, Jun 21 2007

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Last modified April 17 05:12 EDT 2021. Contains 343059 sequences. (Running on oeis4.)