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A283969 a(n) = n + 1 + Sum_({k=0..n} floor((n-k)/r, where r = (3+sqrt(5))/2). 4
1, 4, 10, 18, 29, 43, 59, 78, 99, 123, 150, 179, 211, 246, 283, 323, 365, 410, 458, 508, 561, 616, 674, 735, 798, 864, 933, 1004, 1078, 1154, 1233, 1315, 1399, 1486, 1576, 1668, 1763, 1860, 1960, 2063, 2168, 2276, 2386, 2499, 2615, 2733, 2854, 2978, 3104 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This is column 1 of the transposable interspersion A283938.

LINKS

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

FORMULA

a(n) = n + 1 + Sum_({k=0..n} floor((n-k)/r, where r = (3+sqrt(5))/2).

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) a(n) = if(n<1, 1, a(n - 1) + 1 + floor(n*(3 + sqrt(5))/2));

for(n = 0, 50, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 19 2017

(Python)

import math

from sympy import sqrt

def a(n) : return 1 if n<1 else a(n - 1) + 1 + int(math.floor(n*(3 + sqrt(5))/2))

print [a(n) for n in range(0, 51)] # Indranil Ghosh, Mar 19 2017

CROSSREFS

Cf. A104457, A283968, A283938, A283961.

Sequence in context: A009880 A197057 A025712 * A022781 A112557 A008246

Adjacent sequences:  A283966 A283967 A283968 * A283970 A283971 A283972

KEYWORD

nonn,easy,changed

AUTHOR

Clark Kimberling, Mar 18 2017

STATUS

approved

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Last modified December 14 15:08 EST 2019. Contains 329979 sequences. (Running on oeis4.)