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Interleaving of (1,2,3,4,5,...), (2,2,2,2,...) and (0,1,3,6,10,...).
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%I #26 Jan 05 2025 13:36:41

%S 1,2,0,2,2,1,3,2,3,4,2,6,5,2,10,6,2,15,7,2,21,8,2,28,9,2,36,10,2,45,

%T 11,2,55,12,2,66,13,2,78,14,2,91,15,2,105,16,2,120,17,2,136,18,2,153,

%U 19,2,171,20,2,190,21,2,210,22,2,231,23,2,253,24,2,276,25,2,300,26,2

%N Interleaving of (1,2,3,4,5,...), (2,2,2,2,...) and (0,1,3,6,10,...).

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,3,0,0,-3,0,0,1).

%F G.f.: -(2*x^7+x^5-4*x^4-x^3+2*x+1) / ((x-1)^3*(x^2+x+1)^3). - _Colin Barker_, Jul 31 2013

%p a := proc(n) if n mod 3 = 0 then RETURN(n/3+1) fi: if n mod 3 = 1 then RETURN(2) fi: if n mod 3 = 2 then RETURN(((n-2)/3)*((n-2)/3+1)/2) fi: end: for n from 0 to 150 do printf(`%d,`,a(n)) od:

%t Flatten[ Table[ {n, 2, n(n - 1)/2}, {n, 1, 27}]]

%t With[{nn=30},Riffle[Riffle[Range[nn],Accumulate[Range[0,nn]],{2,-1,2}],2,{2,-1,3}]] (* _Harvey P. Dale_, May 20 2013 *)

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Jun 18 2003

%E More terms from _James A. Sellers_ and _Robert G. Wilson v_, Jun 21 2003