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

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%I A131242 #37 Nov 03 2018 12:03:44
%S A131242 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 A131242 30,33,36,39,42,45,48,51,54,57,60,64,68,72,76,80,84,88,92,96,100,105,
%U A131242 110,115,120,125,130,135,140,145,150,156,162,168,174,180,186,192,198
%N A131242 Partial sums of A059995: a(n) = sum_{k=0..n} floor(k/10).
%C A131242 Complementary with A130488 regarding triangular numbers, in that A130488(n)+10*a(n)=n(n+1)/2=A000217(n).
%H A131242 G. C. Greubel, <a href="/A131242/b131242.txt">Table of n, a(n) for n = 0..1000</a>
%H A131242 <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 A131242 a(n) = (1/2)*floor(n/10)*(2n-8-10*floor(n/10)).
%F A131242 a(n) = A059995(n)*(2n-8-10*A059995(n))/2.
%F A131242 a(n) = (1/2)*A059995(n)*(n-8+A010879(n)).
%F A131242 a(n) = (n-A010879(n))*(n+A010879(n)-8)/20.
%F A131242 G.f.: x^10/((1-x^10)(1-x)^2).
%F A131242 From _Philippe Deléham_, Mar 27 2013: (Start)
%F A131242 a(10n)   = A051624(n).
%F A131242 a(10n+1) = A135706(n).
%F A131242 a(10n+2) = A147874(n+1).
%F A131242 a(10n+3) = 2*A005476(n).
%F A131242 a(10n+4) = A033429(n).
%F A131242 a(10n+5) = A202803(n).
%F A131242 a(10n+6) = A168668(n).
%F A131242 a(10n+7) = 2*A147875(n).
%F A131242 a(10n+8) = A135705(n).
%F A131242 a(10n+9) = A124080(n). (End)
%F A131242 a(n) = A008728(n-10) for n>= 10. - _Georg Fischer_, Nov 03 2018
%e A131242 As square array :
%e A131242     0,   0,   0,   0,   0,   0,   0,   0,   0,    0
%e A131242     1,   2,   3,   4,   5,   6,   7,   8,   9,   10
%e A131242    12,  14,  16,  18,  20,  22,  24,  26,  28,   30
%e A131242    33,  36,  39,  42,  45,  48,  51,  54,  57,   60
%e A131242    64,  68,  72,  76,  80,  84,  88,  92,  96,  100
%e A131242   105, 110, 115, 120, 125, 130, 135, 140, 145,  150
%e A131242   156, 162, 168, 174, 180, 186, 192, 198, 204,  210
%e A131242 ... - _Philippe Deléham_, Mar 27 2013
%t A131242 Table[(1/2)*Floor[n/10]*(2*n - 8 - 10*Floor[n/10]), {n,0,50}] (* _G. C. Greubel_, Dec 13 2016 *)
%t A131242 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 A131242 (PARI) for(n=0,50, print1((1/2)*floor(n/10)*(2n-8-10*floor(n/10)), ", ")) \\ _G. C. Greubel_, Dec 13 2016
%o A131242 (PARI) a(n)=my(k=n\10); k*(n-5*k-4) \\ _Charles R Greathouse IV_, Dec 13 2016
%Y A131242 Cf. A008728, A059995, A010879, A002266, A130488, A000217, A002620, A130518, A130519, A130520, A174709, A174738, A118729, A218470.
%K A131242 nonn,easy
%O A131242 0,12
%A A131242 _Hieronymus Fischer_, Jun 21 2007