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A283968 a(n) = a(n-1) + 1 + floor(n*(3 + sqrt(5))/2), a(0) = 1.

%I A283968 #15 May 07 2021 09:10:55
%S A283968 1,2,3,5,7,9,12,15,19,23,27,32,37,42,48,54,61,68,75,83,91,100,109,118,
%T A283968 128,138,148,159,170,182,194,206,219,232,245,259,273,288,303,318,334,
%U A283968 350,367,384,401,419,437,455,474,493,513,533,553,574,595,617,639
%N A283968 a(n) = a(n-1) + 1 + floor(n*(3 + sqrt(5))/2), a(0) = 1.
%C A283968 This is row 1 of the transposable interspersion A283938.
%H A283968 Clark Kimberling, <a href="/A283968/b283968.txt">Table of n, a(n) for n = 0..1000</a>
%F A283968 a(n) = a(n-1) + 1 + floor(n*(3 + sqrt(5))/2), a(0) = 1.
%t A283968 r = GoldenRatio^2; z = 120;
%t A283968 s[0] = 1; s[n_] := s[n] = s[n - 1] + 1 + Floor[n*r];
%t A283968 Table[n + 1 + Sum[Floor[(n - k)/r], {k, 0, n}], {n, 0, z}] (* A283968 *)
%t A283968 Table[s[n], {n, 0, z}] (* A283969 *)
%o A283968 (PARI) r = (3 + sqrt(5))/2;
%o A283968 a(n) = n + 1 + sum(k=0, n, floor((n - k)/r));
%o A283968 for(n=0, 30, print1(a(n),", ")) \\ _Indranil Ghosh_, Mar 19 2017
%o A283968 (Python)
%o A283968 from sympy import sqrt
%o A283968 import math
%o A283968 def a(n):
%o A283968     return n + 1 + sum([int(math.floor((n - k)/r)) for k in range(n + 1)])
%o A283968 print([a(n) for n in range(61)]) # _Indranil Ghosh_, Mar 19 2017
%Y A283968 Cf. A104457, A283938, A283961, A283969.
%K A283968 nonn,easy
%O A283968 0,2
%A A283968 _Clark Kimberling_, Mar 18 2017