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

1, 2, 3, 5, 7, 9, 12, 15, 19, 23, 27, 32, 37, 42, 48, 54, 61, 68, 75, 83, 91, 100, 109, 118, 128, 138, 148, 159, 170, 182, 194, 206, 219, 232, 245, 259, 273, 288, 303, 318, 334, 350, 367, 384, 401, 419, 437, 455, 474, 493, 513, 533, 553, 574, 595, 617, 639

Offset

0,2

Comments

This is row 1 of the transposable interspersion A283938.

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Formula

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

Mathematica

r = GoldenRatio^2; z = 120;
s[0] = 1; s[n_] := s[n] = s[n - 1] + 1 + Floor[n*r];
Table[n + 1 + Sum[Floor[(n - k)/r], {k, 0, n}], {n, 0, z}] (* A283968 *)
Table[s[n], {n, 0, z}] (* A283969 *)

Prog

(PARI) r = (3 + sqrt(5))/2;
a(n) = n + 1 + sum(k=0, n, floor((n - k)/r));
for(n=0, 30, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 19 2017
(Python)
from sympy import sqrt
import math
def a(n):
    return n + 1 + sum([int(math.floor((n - k)/r)) for k in range(n + 1)])
print([a(n) for n in range(61)]) # Indranil Ghosh, Mar 19 2017

Crossrefs

Cf. A104457, A283938, A283961, A283969.

Sequence in context: A022786 A005704 A022782 * A025692 A137285 A062441

Adjacent sequences: A283965 A283966 A283967 * A283969 A283970 A283971

Keyword

nonn,easy

Author

Clark Kimberling, Mar 18 2017

Status

approved