

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
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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 nth 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 nth 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(n1) +2*a(n2) 2*a(n3) a(n4) +a(n5).
G..f: ( 726*x^2+x^4 ) / ( (1+x)^2*(x1)^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



