A280089 a(n) = 4*n^3 - 3*n + 1.

1, 2, 27, 100, 245, 486, 847, 1352, 2025, 2890, 3971, 5292, 6877, 8750, 10935, 13456, 16337, 19602, 23275, 27380, 31941, 36982, 42527, 48600, 55225, 62426, 70227, 78652, 87725, 97470, 107911, 119072, 130977, 143650, 157115, 171396, 186517, 202502, 219375

Offset

0,2

Links

Daniel Suteu, Table of n, a(n) for n = 0..750

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

Formula

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

Product_{k >= 1} A033430(k)/a(k) = Pi.

From Elmo R. Oliveira, Sep 08 2025: (Start)

G.f.: (1 - 2*x + 25*x^2)/(1 - x)^4.

E.g.f.: (1 + x + 12*x^2 + 4*x^3)*exp(x).

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

Mathematica

Table[4n^3 - 3n + 1, {n, 0, 39}] (* Alonso del Arte, Dec 25 2016 *)

Prog

(PARI) a(n) = (2*n-1)^2*(n+1)

Crossrefs

Cf. A033430.

Sequence in context: A206585 A046735 A038625 * A041801 A166942 A119351

Adjacent sequences: A280086 A280087 A280088 * A280090 A280091 A280092

Keyword

nonn,easy

Author

Daniel Suteu, Dec 25 2016

Status

approved