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

0,2

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).

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

Mathematica

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

Prog

(Haskell)
a257083 n = a257083_list !! n
a257083_list = scanl1 (+) a257088_list
(PARI) vector(60, n, n--; (6*n*(n+1)+(2*n+1)*(-1)^n+7)/8) \\ Bruno Berselli, Jan 05 2016
(Magma) [(6*n*(n+1) + (2*n+1)*(-1)^n + 7)/8 : n in [0..60]]; // Wesley Ivan Hurt, Oct 30 2022

Crossrefs

Cf. A246695 (partial sums), A257088.

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

Sequence in context: A354975 A280228 A254057 * A054974 A072481 A032471

Adjacent sequences: A257080 A257081 A257082 * A257084 A257085 A257086

Keyword

nonn,easy

Author

Reinhard Zumkeller, Apr 17 2015

Status

approved