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A257083 Partial sums of A257088. 6
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 (list; graph; refs; listen; history; text; internal format)
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)

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

CROSSREFS

Cf. A246695 (partial sums), A257088.

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

Sequence in context: A043548 A280228 A254057 * A054974 A072481 A032471

Adjacent sequences:  A257080 A257081 A257082 * A257084 A257085 A257086

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Apr 17 2015

STATUS

approved

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Last modified November 16 22:43 EST 2018. Contains 317275 sequences. (Running on oeis4.)