%I #41 Sep 08 2022 08:45:23

%S 1,3,7,10,16,21,29,36,46,55,67,78,92,105,121,136,154,171,191,210,232,

%T 253,277,300,326,351,379,406,436,465,497,528,562,595,631,666,704,741,

%U 781,820,862,903,947,990,1036,1081,1129,1176,1226,1275,1327,1378,1432

%N a(n) = sum{k=1 to n} (A114112(k)). (For n>=2, a(n) = sum{k=1 to n} (A014681(k)) =sum{k=1 to n} (A103889(k)).).

%C a(n) is not divisible by (A114112(n+1)).

%C Sequence is A130883 union A014105 - {0,2}. - _Anthony Hernandez_, Sep 08 2016

%H Vincenzo Librandi, <a href="/A114113/b114113.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).

%F a(1)=1. a(2n) = n*(2n+1). a(2n+1) = 2n^2 +3n +2.

%F From _R. J. Mathar_, Nov 04 2008: (Start)

%F a(n) = A026035(n+1) - A026035(n), n>1.

%F G.f.: x(1+x+x^2-2x^3+x^4)/((1+x)(1-x)^3).

%F a(n) = 2*a(n-1)-2*a(n-3)+a(n-4), n>5. (End)

%F This is (essentially) 1 + A084265, - _N. J. A. Sloane_, Mar 12 2018

%t Join[{1}, LinearRecurrence[{2, 0, -2, 1}, {3, 7, 10, 16}, 52]] (* _Jean-François Alcover_, Sep 22 2017 *)

%t CoefficientList[Series[(1 + x + x^2 -2 x^3 + x^4)/((1 + x) (1 - x)^3), {x, 0, 60}], x] (* _Vincenzo Librandi_, Mar 13 2018 *)

%o (Magma) I:=[1,3,7,10,16]; [n le 5 select I[n] else 2*Self(n-1)-2*Self(n-3)+Self(n-4): n in [1..60]]; // _Vincenzo Librandi_, Mar 13 2018

%o (Python)

%o def A114113(n): return 1 if n == 1 else (m:=n//2)*(n+1) + (n+1-m)*(n-2*m) # _Chai Wah Wu_, May 24 2022

%Y Cf. A014105, A014681, A026035, A084265, A103889, A114112.

%K easy,nonn

%O 1,2

%A _Leroy Quet_, Nov 13 2005

%E More terms from _R. J. Mathar_, Aug 31 2007