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A319007 Sum of the next n nonnegative integers repeated (A004526). 2
0, 1, 5, 14, 29, 51, 82, 124, 178, 245, 327, 426, 543, 679, 836, 1016, 1220, 1449, 1705, 1990, 2305, 2651, 3030, 3444, 3894, 4381, 4907, 5474, 6083, 6735, 7432, 8176, 8968, 9809, 10701, 11646, 12645, 13699, 14810, 15980, 17210, 18501, 19855, 21274, 22759, 24311, 25932 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

After 29, all terms are composite.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-7,8,-7,4,-1).

FORMULA

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

a(n) = -a(-n) = 4*a(n-1) - 7*a(n-2) + 8*a(n-3) - 7*a(n-4) + 4*a(n-5) - a(n-6).

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

a(n) = A319006(n) - n.

a(n) = (n^3 - 2*n + Chi(n))/4 where Chi(n) = A101455(n). - Peter Luschny, Sep 09 2018

EXAMPLE

Next n nonnegative integers repeated: Sums:

0, ...................................... 0

0, 1, ................................... 1

1, 2, 2, ................................ 5

3, 3, 4, 4, ............................. 14

5, 5, 6, 6, 7, .......................... 29

7, 8, 8, 9, 9, 10, ...................... 51, etc.

MAPLE

a := n -> (n^3 - 2*n + (-(n mod 2))^binomial(n, 2))/4;

seq(a(n), n=1..47); # Peter Luschny, Sep 09 2018

MATHEMATICA

Table[(2 n (n^2 - 2) + (1 - (-1)^n) (-1)^((n-1)/2))/8, {n, 1, 50}]

PROG

(Magma) [Integers()! (n*(n^2-2)+(-(n mod 2))^(n*(n-1)/2))/4: n in [1..50]];

(PARI) concat(0, Vec(x^2*(1 + x + x^2)/((1 + x^2)*(1 - x)^4) + O(x^50))) \\ Colin Barker, Sep 10 2018

CROSSREFS

Cf. A004526, A101455, A319006.

Sum of the next n nonnegative integers: A027480.

Sequence in context: A005918 A321178 A256666 * A211651 A299291 A019262

Adjacent sequences: A319004 A319005 A319006 * A319008 A319009 A319010

KEYWORD

nonn,easy

AUTHOR

Bruno Berselli, Sep 07 2018

STATUS

approved

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Last modified November 30 17:37 EST 2022. Contains 358453 sequences. (Running on oeis4.)