A283938 -id:A283938 - cp's OEIS frontend

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

Clark Kimberling, Mar 18 2017

This is row 1 of the transposable interspersion A283938.

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

Cf. A104457, A283938, A283961, A283969.

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 *)

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

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

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

A283969 a(n) = n + 1 + Sum_{k=0..n} floor((n-k)/r), where r = (3+sqrt(5))/2.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Mar 18 2017

This is column 1 of the transposable interspersion A283938.

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

Cf. A104457, A283968, A283938, A283961.

Partial sums of A026352.

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 *)

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

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(51)]) # Indranil Ghosh, Mar 19 2017

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

cp's OEIS Frontend

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

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