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a(n) = ceiling(n/24) + ceiling((n+1)/24).
0

%I #12 Apr 05 2018 17:52:51

%S 1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,4,4,4,4,4,4,4,4,4,

%T 4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,

%U 6,6,6,6,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,10,10,10,10,10

%N a(n) = ceiling(n/24) + ceiling((n+1)/24).

%F Euler transform of length 24 sequence [ 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]. - _Michael Somos_, Aug 07 2005

%F Expansion of 1/((x^2+1)*(x^4+1)*(x^8-x^4+1)*(x^4-x^2+1)*(x^2-x+1)*(1+x^2+x)*(x-1)^2).

%F G.f.: (1 - x^2) / ((1 - x)^2 * (1 - x^24)).

%F a(n) = -a(-24-n) for all n in Z. - _Michael Somos_, May 05 2015

%e G.f. = 1 + 2*x + 2*x^2 + 2*x^3 + 2*x^4 + 2*x^5 + 2*x^6 + 2*x^7 + 2*x^8 + ...

%p seriestolist(series(1/((x^2+1)*(x^4+1)*(x^8-x^4+1)*(x^4-x^2+1)*(x^2-x+1)*(1+x^2+x)*(x-1)^2), x=0,150));

%t a[ n_] := Ceiling[n / 24] + Ceiling[(n + 1) / 24]; (* _Michael Somos_, May 05 2015 *)

%t Total/@Partition[Ceiling[Range[0,110]/24],2,1] (* _Harvey P. Dale_, Apr 05 2018 *)

%o (PARI) {a(n) = ceil(n / 24) + ceil((n+1) / 24)}; /* _Michael Somos_, Aug 07 2005 */

%K nonn

%O 0,2

%A _Creighton Dement_, Jul 24 2005