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A076307 a(n) = n+min(2*floor(a(n-1)/2), 3*floor(a(n-1)/3)) for n > 1, a(1)=1. 0

%I

%S 1,2,3,6,11,15,21,28,36,46,56,66,79,92,105,120,137,153,171,190,210,

%T 232,254,276,301,326,351,378,407,435,465,496,528,562,596,630,667,704,

%U 741,780,821,861,903,946,990,1036,1082,1128,1177,1226,1275,1326,1379,1431

%N a(n) = n+min(2*floor(a(n-1)/2), 3*floor(a(n-1)/3)) for n > 1, a(1)=1.

%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1).

%F a(n) = n*(n-1)/2 + b(n) where b repeats the period (1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0) of length 12.

%F a(n) = +2*a(n-1) -a(n-2) +a(n-12) -2*a(n-13) +a(n-14).

%F G.f.: -x*(1+2*x^4-x^5+2*x^6+x^7+x^8+2*x^9+2*x^12+2*x^3) / ( (1+x) *(1+x^2) *(1+x+x^2) *(x^2-x+1) *(x^4-x^2+1) *(x-1)^3 ).

%t LinearRecurrence[{2,-1,0,0,0,0,0,0,0,0,0,1,-2,1},{1,2,3,6,11,15,21,28,36,46,56,66,79,92},60] (* _Harvey P. Dale_, Nov 29 2013 *)

%o (MAGMA) [ n eq 1 select 1 else n+Min(2*Floor(Self(n-1)/2), 3*Floor(Self(n-1)/3)) : n in [1..60] ]; // _Klaus Brockhaus_, Dec 03 2010

%o (MAGMA) b:=func< n | [1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0][(n mod 12)+1] >; [ n*(n-1)/2+b(n-1): n in [1..60] ]; // _Klaus Brockhaus_, Dec 03 2010

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, Nov 06 2002

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Last modified February 20 04:25 EST 2020. Contains 332063 sequences. (Running on oeis4.)