A305290 Numbers k such that 4*k + 1 is a perfect cube, sorted by absolute values.
0, -7, 31, -86, 182, -333, 549, -844, 1228, -1715, 2315, -3042, 3906, -4921, 6097, -7448, 8984, -10719, 12663, -14830, 17230, -19877, 22781, -25956, 29412, -33163, 37219, -41594, 46298, -51345, 56745, -62512, 68656, -75191, 82127, -89478, 97254, -105469, 114133, -123260, 132860
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (-3,-2,2,3,1).
Crossrefs
Programs
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Maple
seq(coeff(series(x^2*(-7+10*x-7*x^2)/((1-x)*(1+x)^4), x,50),x,n),n=1..45); # Muniru A Asiru, May 31 2018
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Mathematica
LinearRecurrence[{-3, -2, 2, 3, 1}, {0, -7, 31, -86, 182}, 45] (* Jean-François Alcover, Jun 04 2018 *) -
PARI
concat(0, Vec(-x^2*(7 - 10*x + 7*x^2) / ((1 - x)*(1 + x)^4) + O(x^40))) \\ Colin Barker, Jun 04 2018
Formula
G.f.: x^2*(-7 + 10*x - 7*x^2)/((1 - x)*(1 + x)^4).
a(n) = -3*a(n-1) - 2*a(n-2) + 2*a(n-3) + 3*a(n-4) + a(n-5).
a(n) = (-1 - A016755(n-1)*(-1)^n)/4.
a(n) + a(-n) = (-1)^n*2^((1-(-1)^n)/2).
(n - 2)*(4*n^2 - 16*n + 19)*a(n) + (12*n^2 - 36*n + 31)*a(n-1) - (n - 1)*(4*n^2 - 8*n + 7)*a(n-2) = 0.
From Colin Barker, May 30 2018: (Start)
a(n) = n*(4*n^2 + 6*n + 3)/2 for n even.
a(n) = -(n + 1)*(4*n^2 + 2*n + 1)/2 for n odd.
(End)