A079588 a(n) = (n+1)*(2*n+1)*(4*n+1).

1, 30, 135, 364, 765, 1386, 2275, 3480, 5049, 7030, 9471, 12420, 15925, 20034, 24795, 30256, 36465, 43470, 51319, 60060, 69741, 80410, 92115, 104904, 118825, 133926, 150255, 167860, 186789, 207090, 228811, 252000, 276705, 302974, 330855, 360396, 391645

Offset

0,2

Comments

Apart from offset, same as A100147.

References

Robert Tijdeman, Some applications of Diophantine approximation, pp. 261-284 of Surveys in Number Theory (Urbana, May 21, 2000), ed. M. A. Bennett et al., Peters, 2003.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

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

Formula

Sum_{n>=0} 1/a(n) = Pi/3 (cf. Tijdeman).

From L. Edson Jeffery, Mar 25 2013: (Start)

G.f.: (1+26*x+21*x^2)/(1-x)^4.

Sum_{n>=0} a(n)/2^n = 308; Sum_{n>=0} (-1)^n*a(n)/2^n = -4/3. (End)

a(n) = 8*n^3 + 14*n^2 + 7*n + 1. - Reinhard Zumkeller, Jun 08 2015

Sum_{n>=0} (-1)^n/a(n) = log(2)/3 - Pi/2 + sqrt(2)*Pi/3 + 2*sqrt(2)*arcsin(1)/3. - Amiram Eldar, Jan 13 2021

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, Jun 23 2021

From Elmo R. Oliveira, Dec 02 2025: (Start)

E.g.f.: exp(x)*(1 + 29*x + 38*x^2 + 8*x^3).

a(n) = A000384(n+1)*A016813(n). (End)

Mathematica

Table[(n + 1)*(2*n + 1)*(4*n + 1), {n, 0, 40}] (* Amiram Eldar, Jan 13 2021 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 30, 135, 364}, 40] (* Harvey P. Dale, Aug 01 2022 *)

Prog

(Haskell)
a079588 n = product $ map ((+ 1) . (* n)) [1, 2, 4]
-- Reinhard Zumkeller, Jun 08 2015

Crossrefs

Cf. A000384, A011199, A016813, A100147, A258721 (first differences).

Sequence in context: A044743 A221522 A291582 * A100147 A117750 A348828

Adjacent sequences: A079585 A079586 A079587 * A079589 A079590 A079591

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 26 2003

Status

approved