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A085027 a(n) = (4*n+3)*(4*n+7). 4
21, 77, 165, 285, 437, 621, 837, 1085, 1365, 1677, 2021, 2397, 2805, 3245, 3717, 4221, 4757, 5325, 5925, 6557, 7221, 7917, 8645, 9405, 10197, 11021, 11877, 12765, 13685, 14637, 15621, 16637, 17685, 18765, 19877, 21021, 22197, 23405, 24645, 25917, 27221, 28557, 29925, 31325, 32757, 34221 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

1 = 3/7 + Sum(n=1,inf.,16/a(n)) = 3/7 + 16/77 + 16/165 + 16/285...+...; with partial sums: 3/7, 7/11, 11/15, 15/19, 19/23...(4n+3)/(4n+7)...==>1

With A003185(n)=(1+4*n)*(5+4*n), a bisection of A078371(n) which is a bisection of A061037(n+2).

A quadrisection of A061037(n+2).After A002378(n), A003185(n) and A000466(n+1). - Paul Curtz, Mar 30 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 16*n^2+40*n+21. - Vincenzo Librandi, Aug 13 2011

From Colin Barker, Jul 11 2012: (Start)

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

G.f.: (21+14*x-3*x^2)/(1-x)^3. (End)

E.g.f.: (21 +56*x +16*x^2)*exp(x). - G. C. Greubel, Sep 20 2018

EXAMPLE

21 = (3)(7), 77 = (7)(11), 165 = (11)(15), 285 = (15)(19), 437 = (19)(23)...

MATHEMATICA

Table[(4*n + 3) (4*n + 7), {n, 0, 45}]

PROG

(MAGMA) [16*n^2+40*n+21: n in [0..35]]; // Vincenzo Librandi, Aug 13 2011

(PARI) a(n)=(4*n+3)*(4*n+7) \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Sequence in context: A296155 A218960 A218955 * A143206 A182754 A045559

Adjacent sequences:  A085024 A085025 A085026 * A085028 A085029 A085030

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Jun 19 2003

STATUS

approved

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Last modified September 27 19:04 EDT 2020. Contains 337388 sequences. (Running on oeis4.)