cp's OEIS Frontend

A249013 a(n) = floor( (n-1) * (n+4) / 10 ).

%I A249013 #26 Sep 08 2022 08:46:10
%S A249013 0,0,1,2,3,5,6,8,10,12,15,17,20,23,26,30,33,37,41,45,50,54,59,64,69,
%T A249013 75,80,86,92,98,105,111,118,125,132,140,147,155,163,171,180,188,197,
%U A249013 206,215,225,234,244,254,264,275,285,296,307,318,330,341,353,365
%N A249013 a(n) = floor( (n-1) * (n+4) / 10 ).
%C A249013 A028557(n) without the least significant digit. - _R. J. Mathar_, Aug 11 2021
%H A249013 G. C. Greubel, <a href="/A249013/b249013.txt">Table of n, a(n) for n = 1..2500</a>
%H A249013 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,1,-2,1).
%F A249013 G.f.: x^3 * (1 + x^3 - x^4) / ((1 - x)^2 * (1 - x^5)) = x^3*(1+x^3-x^4)/ ( (1-x)^3*(1+x+x^2+x^3+x^4)).
%F A249013 a(n) = a(-3-n) for all n in Z.
%F A249013 a(n) = a(n-5) + n-1 for all n in Z.
%F A249013 a(n) + a(n+4) = min( a(n+1) + a(n+3), a(n+2) + a(n+2) ) + 1 for all n in Z.
%F A249013 A249020(n) = a(n+1) + 1 for all n in Z. - _Michael Somos_, Jan 09 2015
%e A249013 G.f. = x^3 + 2*x^4 + 3*x^5 + 5*x^6 + 6*x^7 + 8*x^8 + 10*x^9 + 12*x^10 + ...
%t A249013 a[ n_] := Quotient[ (n - 1) (n + 4), 10];
%t A249013 LinearRecurrence[{2, -1, 0, 0, 1, -2, 1}, {0, 0, 1, 2, 3, 5, 6}, 60] (* or *) CoefficientList[Series[x^2 (1 + x^3 - x^4) / ((1 - x)^2 (1 - x^5)), {x, 0, 60}], x] (* _Vincenzo Librandi_, Jan 10 2015 *)
%o A249013 (PARI) {a(n) = (n-1) * (n+4) \ 10};
%o A249013 (PARI) {a(n) = if( n<-1, n = -3-n); -(n<1) + polcoeff( x^3*(1 + x^3 - x^4) / ((1 - x)^2 * (1 - x^5)) + x * O(x^n), n)};
%o A249013 (Magma) [Floor((n-1)*(n+4)/10): n in [1..60]]; // _Vincenzo Librandi_, Jan 10 2015
%Y A249013 Cf. A249020, A028557.
%K A249013 nonn,easy
%O A249013 1,4
%A A249013 _Michael Somos_, Oct 19 2014