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%I #21 Feb 02 2023 15:25:25
%S 0,1,4,9,17,26,37,50,66,83,102,123,147,172,199,228,260,293,328,365,
%T 405,446,489,534,582,631,682,735,791,848,907,968,1032,1097,1164,1233,
%U 1305,1378,1453,1530,1610,1691,1774,1859,1947,2036,2127,2220,2316,2413,2512
%N a(n) = n^2 + floor(n/4).
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,1,-2,1).
%F a(n) = A002378(n)-A057353(n) = A035608(n)-A002265(n+2) = A000290(n)+A002265(n);
%F a(n+1) - a(n) = A047624(n+2).
%F a(n) = floor((n + 1/8)^2).
%F a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6) for n>5.
%F G.f.: x*(1+2*x+2*x^2+3*x^3)/((1+x)*(x^2+1)*(1-x)^3). - _R. J. Mathar_, Feb 27 2010
%F a(n) = (8*n^2+2*n-3+i^(2*n)+(1+i)*i^(-n)+(1-i)*i^n)/8 where i=sqrt(-1). - _Wesley Ivan Hurt_, Jun 04 2016
%p A173562:=n->floor((n + 1/8)^2): seq(A173562(n), n=0..80); # _Wesley Ivan Hurt_, Jun 04 2016
%t Table[n^2+Floor[n/4],{n,0,50}] (* or *) LinearRecurrence[{2,-1,0,1,-2,1}, {0,1,4,9,17,26}, 50] (* _Harvey P. Dale_, Nov 25 2011 *)
%o (PARI) a(n)=n^2+n\4 \\ _Charles R Greathouse IV_, Oct 16 2015
%o (Magma) [Floor((n + 1/8)^2) : n in [0..80]]; // _Wesley Ivan Hurt_, Jun 04 2016
%o (Python)
%o def A173562(n): return n**2+(n>>2) # _Chai Wah Wu_, Feb 02 2023
%Y Cf. A000290, A002265, A002378, A035608, A047624, A057353.
%K nonn,easy
%O 0,3
%A _Reinhard Zumkeller_, Feb 21 2010
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