%I #15 May 07 2021 09:10:55

%S 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 128,138,148,159,170,182,194,206,219,232,245,259,273,288,303,318,334,

%U 350,367,384,401,419,437,455,474,493,513,533,553,574,595,617,639

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

%C This is row 1 of the transposable interspersion A283938.

%H Clark Kimberling, <a href="/A283968/b283968.txt">Table of n, a(n) for n = 0..1000</a>

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

%t r = GoldenRatio^2; z = 120;

%t s[0] = 1; s[n_] := s[n] = s[n - 1] + 1 + Floor[n*r];

%t Table[n + 1 + Sum[Floor[(n - k)/r], {k, 0, n}], {n, 0, z}] (* A283968 *)

%t Table[s[n], {n, 0, z}] (* A283969 *)

%o (PARI) r = (3 + sqrt(5))/2;

%o a(n) = n + 1 + sum(k=0, n, floor((n - k)/r));

%o for(n=0, 30, print1(a(n),", ")) \\ _Indranil Ghosh_, Mar 19 2017

%o (Python)

%o from sympy import sqrt

%o import math

%o def a(n):

%o return n + 1 + sum([int(math.floor((n - k)/r)) for k in range(n + 1)])

%o print([a(n) for n in range(61)]) # _Indranil Ghosh_, Mar 19 2017

%Y Cf. A104457, A283938, A283961, A283969.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Mar 18 2017