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A173294 Values of 16*n^2+24*n+7, n>=0, each duplicated. 3
7, 7, 47, 47, 119, 119, 223, 223, 359, 359, 527, 527, 727, 727, 959, 959, 1223, 1223, 1519, 1519, 1847, 1847, 2207, 2207, 2599, 2599, 3023, 3023, 3479, 3479, 3967, 3967, 4487, 4487, 5039, 5039, 5623, 5623, 6239, 6239, 6887, 6887, 7567, 7567, 8279, 8279, 9023, 9023, 9799, 9799, 10607, 10607, 11447, 11447, 12319, 12319, 13223, 13223, 14159, 14159, 15127, 15127, 16127 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The Leibniz series for Pi/4 involves 1, -1/3, 1/5, -1/7, 1/9, -1/11, .. inverses of the odd numbers. The first differences of this sequence of fractions are -4/3, 8/15, -12/35, 16/63, -20/99, 24/143,... = (-1)^(n+1)*A008586(n+1)/A000466(n+1).

a(n) is the difference of the n-th denominator and numerator, A000466(n+1)+(-1)^n*A008586(n+1). (Note that A000466 is a bisection of A005563, which establishes a very distant relation between this sequence and the Lyman series.)

If one would add the n-th denominator and numerator, -1, 23, 23, 79, 79, 167, 167, 287, 287, 439,...(duplicated values of 16n^2+40n+23 and a -1) would result.

LINKS

Table of n, a(n) for n=0..62.

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

FORMULA

a(n) = +a(n-1) +2*a(n-2) -2*a(n-3) -a(n-4) +a(n-5).

G..f: ( -7-26*x^2+x^4 ) / ( (1+x)^2*(x-1)^3 ).

a(2n) = a(2n+1) = 16n^2+24n+7.

CROSSREFS

Sequence in context: A219399 A219447 A271064 * A165828 A161343 A038273

Adjacent sequences:  A173291 A173292 A173293 * A173295 A173296 A173297

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Feb 15 2010

STATUS

approved

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Last modified December 11 19:09 EST 2017. Contains 295919 sequences.