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a(n) = (A000045(n)+A173432(n))/2.
2

%I #13 Jun 11 2019 20:02:17

%S 1,1,2,2,3,4,7,11,18,28,45,72,117,189,306,494,799,1292,2091,3383,5474,

%T 8856,14329,23184,37513,60697,98210,158906,257115,416020,673135,

%U 1089155,1762290,2851444,4613733,7465176,12078909,19544085,31622994,51167078,82790071,133957148

%N a(n) = (A000045(n)+A173432(n))/2.

%C Also the NW-SE diagonal sums of A173398.

%H Robert Israel, <a href="/A173433/b173433.txt">Table of n, a(n) for n = 1..4783</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,2,0,-1).

%F a(n) = 1/2-(-1)^n/6+A057079(n+4)/6+A000045(n)/2 with g.f. -x*(-1+x+x^4)/ ((x-1) * (1+x) * (x^2+x-1) * (x^2-x+1)). - _R. J. Mathar_, Mar 04 2010

%p f:=gfun:-rectoproc({-a(n) - a(n + 1) + a(n + 2) - a(n + 3) - a(n + 4) + a(n + 5) + 1, a(0) = 0, a(1) = 1, a(2) = 1, a(3) = 2, a(4) = 2, a(5) = 3},a(n),remember):

%p map(f, [$1..50]); # _Robert Israel_, Jun 11 2019

%t CoefficientList[Series[-x*(-1+x+x^4)/((x-1)*(1+x)*(x^2+x-1)*(x^2-x+1)),{x,0,42}],x] (* _Georg Fischer_, Jun 11 2019 *)

%Y Cf. A112468, A000045, A057079, A173432, A173398.

%K nonn,easy

%O 1,3

%A _Mark Dols_, Feb 18 2010

%E a(35) corrected by _Georg Fischer_, Jun 11 2019