A268201 a(n) = 4*n^3 - 6*n^2 + 3*n - 1.

0, 13, 62, 171, 364, 665, 1098, 1687, 2456, 3429, 4630, 6083, 7812, 9841, 12194, 14895, 17968, 21437, 25326, 29659, 34460, 39753, 45562, 51911, 58824, 66325, 74438, 83187, 92596, 102689, 113490, 125023, 137312, 150381, 164254, 178955, 194508, 210937, 228266, 246519, 265720

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 16 2016

Keywords

• nonn
• easy

Comments

Nonnegative numbers n such that 2*n+1 is a cube.

Or, (y^k-1)/2 for k odd. - N. J. A. Sloane, Mar 05 2022

Examples

			a(1) = 0 because 4*1^3 - 6*1^2 + 3*1 - 1 = 0.
a(2) = 13 because 4*2^3 - 6*2^2 + 3*2 - 1 = 13.
		

References

• H. Brocard, #2158, L'Intermédiaire des Mathématiciens, 10 (1903), 282-283

Links

• Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

Crossrefs

Cf. nonnegative numbers n such that 2*n + k is a cube: A271828 (k=-3), A050492 (k=-1), this sequence (k=1).

Programs

Magma

[((2*n-1)^3-1)/2: n in [0..41]];

Maple

A268201:=n->4*n^3 - 6*n^2 + 3*n - 1: seq(A268201(n), n=1..80); # Wesley Ivan Hurt, Apr 17 2016

Mathematica

Table[((2 n - 1)^3 - 1)/2, {n, 41}] (* or *)
CoefficientList[Series[(13*x + 10*x^2 + x^3)/(-1 + x)^4, {x, 0, 40}],
   x] (* Michael De Vlieger, Apr 16 2016 *)

PARI

lista(nn) = for(n=1, nn, print1(4*n^3-6*n^2+3*n-1, ", ")); \\ Altug Alkan, Apr 17 2016

Formula

G.f.: (13*x + 10*x^2 + x^3)/(-1 + x)^4. - Michael De Vlieger, Apr 16 2016

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4. - Wesley Ivan Hurt, Apr 17 2016