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a(n) = A088828(n) + A157502(n).
0

%I #25 Jan 31 2014 23:26:01

%S 5,11,15,21,25,29,35,39,43,47,53,57,61,65,69,75,79,83,87,91,95,101,

%T 105,109,113,117,121,125,131,135,139,143,147,151,155,159,165,169,173,

%U 177,181,185,189,193,197,203,207,211,215,219,223,227,231,235,239,245

%N a(n) = A088828(n) + A157502(n).

%F Let T(n) be 1 if positive n is a triangular number, else 0; we also define T(0) as 0. Then we can also write this sequence as 1 + 4*n + 2*[T(1) + T(2) ... T(n-1)]. (Other than the special definition for T(0), T(n) is essentially A010054.)

%F The sequence can also be seen visually as

%F 1 + 4

%F 1 + 4 + 6

%F 1 + 4 + 6 + 4

%F 1 + 4 + 6 + 4 + 4

%F 1 + 4 + 6 + 4 + 4 + 6

%F 1 + 4 + 6 + 4 + 4 + 6 + 4

%F 1 + 4 + 6 + 4 + 4 + 6 + 4 + 4

%F 1 + 4 + 6 + 4 + 4 + 6 + 4 + 4 + 4

%F 1 + 4 + 6 + 4 + 4 + 6 + 4 + 4 + 4 + 6...

%t Module[{nn=60,tb},tb=2*Accumulate[Table[If[IntegerQ[(Sqrt[8n+1]-1)/2],1,0],{n,nn}]];Join[{5},Table[1+4i+tb[[i-1]],{i,2,nn}]]] (* _Harvey P. Dale_, Jul 22 2013 *)

%Y Cf. A088828 and A157502. Also alternate generation formula related to A000217, A010054.

%K nonn

%O 1,1

%A _Ed Smiley_, Dec 23 2012