A257083 Partial sums of A257088.

1, 2, 6, 9, 17, 22, 34, 41, 57, 66, 86, 97, 121, 134, 162, 177, 209, 226, 262, 281, 321, 342, 386, 409, 457, 482, 534, 561, 617, 646, 706, 737, 801, 834, 902, 937, 1009, 1046, 1122, 1161, 1241, 1282, 1366, 1409, 1497, 1542, 1634, 1681, 1777, 1826, 1926, 1977

Offset: 0

Author

Reinhard Zumkeller, Apr 17 2015

Keywords

• nonn
• easy

Comments

Equivalently, numbers of the form m*(3*m+2)+1, where m = 0, -1, 1, -2, 2, -3, 3, ... - Bruno Berselli, Jan 05 2016

Also, numbers k such that 3*k-2 is a square. - Bruno Berselli, Jan 30 2018

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A246695 (partial sums), A257088.

Cf. A056109: numbers of the form m*(3*m+2)+1 for nonnegative m.

Programs

Haskell

a257083 n = a257083_list !! n
a257083_list = scanl1 (+) a257088_list

Magma

[(6*n*(n+1) + (2*n+1)*(-1)^n + 7)/8 : n in [0..60]]; // Wesley Ivan Hurt, Oct 30 2022

Mathematica

Table[(6 n (n + 1) + (2 n + 1) (-1)^n + 7)/8, {n, 0, 60}] (* Bruno Berselli, Jan 05 2016 *)

PARI

vector(60, n, n--; (6*n*(n+1)+(2*n+1)*(-1)^n+7)/8) \\ Bruno Berselli, Jan 05 2016

Formula

From Bruno Berselli, Jan 05 2016: (Start)

G.f.: (1 + x + 2*x^2 + x^3 + x^4)/((1 + x)^2*(1 - x)^3).

a(n) = (6*n*(n+1) + (2*n+1)*(-1)^n + 7)/8. (End)

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5). - Wesley Ivan Hurt, Oct 30 2022