A319007 Sum of the next n nonnegative integers repeated (A004526).
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
Offset: 1
Examples
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.
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).
Programs
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Magma
[Integers()! (n*(n^2-2)+(-(n mod 2))^(n*(n-1)/2))/4: n in [1..50]];
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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
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Mathematica
Table[(2 n (n^2 - 2) + (1 - (-1)^n) (-1)^((n-1)/2))/8, {n, 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
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
Comments