A184535 -id:A184535 - cp's OEIS frontend

A279169 a(n) = floor( 4*n^2/5 ).

0, 0, 3, 7, 12, 20, 28, 39, 51, 64, 80, 96, 115, 135, 156, 180, 204, 231, 259, 288, 320, 352, 387, 423, 460, 500, 540, 583, 627, 672, 720, 768, 819, 871, 924, 980, 1036, 1095, 1155, 1216, 1280, 1344, 1411, 1479, 1548, 1620, 1692, 1767, 1843, 1920, 2000, 2080, 2163, 2247

Offset: 0

Bruno Berselli, Dec 07 2016

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-2,1).

Cf. A090223: floor(4*n/5).
Subsequence of A008728, A014601, A118015, A131242.
Cf. similar sequences with closed form floor(k*n^2/5): A118015 (k=1), A033437 (k=2), A184535 (k=3).

Magma
```
[4*n^2 div 5: n in [0..60]];
```

Table[Floor[4 n^2/5], {n, 0, 60}]
LinearRecurrence[{2,-1,0,0,1,-2,1},{0,0,3,7,12,20,28},60] (* Harvey P. Dale, Nov 07 2020 *)

PARI
```
vector(60, n, n--; floor(4*n^2/5))
```
Python
```
[int(4*n**2/5) for n in range(60)]
```
Sage
```
[floor(4*n^2/5) for n in range(60)]
```

O.g.f.: x^2*(3 + x + x^2 + 3*x^3)/((1 - x)^3*(1 + x + x^2 + x^3 + x^4)).
a(n) = a(-n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7).
a(5*m+r) = 4*m*(5*m + 2*r) + a(r), where m >= 0 and 0 <= r < 5. Example: for m=4 and r=3, a(5*4+3) = a(23) = 4*4*(5*4 + 2*3) + a(3) = 416 + 7 = 423.
a(n) = A118015(2*n) = A008728(4*n+2) = A131242(4*n+4) = A014601(floor(2*n^2/5)).
Sum_{n>=2} 1/a(n) = Pi^2/120 + sqrt(29 - 62/sqrt(5))*Pi/8 + 5/16. - Amiram Eldar, Sep 26 2022

A184532 Array, read by rows: T(n,h)=floor[1/{(h+n^3)^(1/3)}], where h=1,2,...,3n^2+3n and {}=fractional part.

Original entry on oeis.org

3, 2, 1, 1, 1, 1, 12, 6, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 13, 9, 7, 5, 4, 4, 3, 3, 3, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 48, 24, 16, 12, 9, 8, 7, 6, 5, 5, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 75, 37, 25, 18, 15, 12, 10, 9, 8, 7, 7, 6, 5, 5, 5, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1

Offset: 1

Clark Kimberling, Jan 16 2011

			First 2 rows:
  3, 2, 1, 1, 1, 1
  12, 6, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Cf. A013942 (analogous array for sqrt(h+n^2)), A184533.

Columns 1 to 6: A033428 (3n^2), A184532=A000290+A007590, A000290 (n^2), A184534, A184535, A080476.

f[n_,h_]:=FractionalPart[(n^3+h)^(1/3)];
g[n_,h_]:=Floor[1/f[n,h]];
Table[Flatten[Table[g[n,h],{n,1,5},{h,1,3n^2+3n}]]]
TableForm[Table[g[n,h],{n,1,5},{h,1,3n^2+3n}]]

T(n,h)=floor[1/{(h+n^3)^(1/3)}], where h=1,2,...,3n^2+3n and {}=fractional part.

cp's OEIS Frontend

A279169 a(n) = floor( 4*n^2/5 ).

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