A132270 -id:A132270 - cp's OEIS frontend

A239831 Floor(7n^2/2) + floor(5n/2) + floor(3n/7).

5, 19, 39, 67, 101, 143, 191, 247, 308, 379, 454, 539, 628, 727, 830, 942, 1060, 1186, 1318, 1458, 1604, 1758, 1917, 2086, 2259, 2442, 2629, 2826, 3027, 3237, 3453, 3677, 3907, 4145, 4389, 4641, 4898, 5165, 5436, 5717, 6002, 6297, 6596, 6904, 7218, 7540

Offset: 1

Katherine Guo, Mar 27 2014

This is a quadratic sequence.

			For n=3, a(3) = floor(7*3^2/2) + floor(5*3/2) + floor(3*3/7) = 39.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Wolfram Alpha, Table of floor(7n^2/2) + floor(5n/2) + floor(3n/7).
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,0,1,-1,-1,1).

[Floor(7*n^2/2) + Floor(5*n/2) + Floor(3*n/7): n in [1..50]]; // Vincenzo Librandi, Mar 29 2014

A239831:=n->floor(7*n^2/2) + floor(5*n/2) + floor(3*n/7); seq(A239831(n), n=1..50); # Wesley Ivan Hurt, Mar 28 2014

Table[Floor[7 n^2/2] + Floor[5 n/2] + Floor[3 n/7], {n, 50}] (* Bruno Berselli, Mar 28 2014 *)

a(n) = (n(7n + 5) + (-1)^n - 1)/2 + A132270(3n + 1). [Bruno Berselli, Mar 28 2014]

a(n) = +a(n-1) +a(n-2) -a(n-3) +a(n-7) -a(n-8) -a(n-9) +a(n-10). [Bruno Berselli, Mar 28 2014]

More terms from Bruno Berselli, Mar 28 2014

A225875 We write the 1 + 4*k numbers once and twice the others.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 4, 5, 6, 6, 7, 7, 8, 8, 9, 10, 10, 11, 11, 12, 12, 13, 14, 14, 15, 15, 16, 16, 17, 18, 18, 19, 19, 20, 20, 21, 22, 22, 23, 23, 24, 24, 25, 26, 26, 27, 27, 28, 28, 29, 30, 30, 31, 31, 32, 32, 33, 34, 34, 35, 35, 36, 36, 37, 38, 38, 39, 39, 40, 40, 41, 42, 42, 43

Offset: 1

José María Grau Ribas, May 19 2013

First differences are periodic with period 7.

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

Cf. A132270.

t = {}; Do[If[Mod[n, 4] == 1, AppendTo[t, n], AppendTo[t, {n, n}]], {n, 50}]; Flatten[t] (* T. D. Noe, May 23 2013 *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1},{1, 2, 2, 3, 3, 4, 4, 5},74] (* Ray Chandler, Aug 26 2015 *)
Table[If[Mod[n, 4] == 1, n, {n, n}], {n, 50}] // Flatten (* or *) Drop[ Flatten[ Table[{n,n},{n,50}]],{1,-1,8}] (* Harvey P. Dale, Feb 03 2019 *)

a(n+1) = 1 + 4*floor(n/7) + [0,1,1,2,2,3,3].
G.f.: x*(1 + x + x^3 + x^5)/((1-x)^2 * (1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).
a(n) = n - floor(3*n/7). - Wesley Ivan Hurt, Sep 29 2017

Corrected, extended, and edited by Ralf Stephan, May 20 2013

cp's OEIS Frontend

A239831 Floor(7n^2/2) + floor(5n/2) + floor(3n/7).

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