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Revision History for A133766

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A133766

a(n) = (4*n+1)*(4*n+3)*(4*n+5).
(history; published version)

#26 by Joerg Arndt at Sun Feb 27 05:46:45 EST 2022

STATUS

reviewed

approved

#25 by Michel Marcus at Sun Feb 27 02:47:33 EST 2022

STATUS

proposed

reviewed

#24 by Amiram Eldar at Sun Feb 27 02:27:51 EST 2022

STATUS

editing

proposed

#23 by Amiram Eldar at Sun Feb 27 01:56:22 EST 2022

DATA

15, 315, 1287, 3315, 6783, 12075, 19575, 29667, 42735, 59163, 79335, 103635, 132447, 166155, 205143, 249795, 300495, 357627, 421575, 492723, 571455, 658155, 753207, 856995, 969903, 1092315, 1224615, 1367187, 1520415, 1684683, 1860375, 2047875, 2247567, 2459835

#22 by Amiram Eldar at Sun Feb 27 01:55:10 EST 2022

CROSSREFS

Cf. A001539, A154633.

#21 by Amiram Eldar at Sun Feb 27 01:54:45 EST 2022

FORMULA

a(0)=15, a(1)=315, a(2)=1287, a(3)=3315; for n>3, a(n) = 4*a(n-1)-) - 6*a(n-2)+ ) + 4*a(n-3)- ) - a(n-4). - _) for n>3. - _Harvey P. Dale_, May 06 2012

#20 by Amiram Eldar at Sun Feb 27 01:54:05 EST 2022

REFERENCES

L. B. W. Jolley, Summation of Series, Dover (, 1961)..

FORMULA

sum(4/((4*m+1)*(4*m+3)*(4*m+5)), m=0..infinity) = (Pi-2)/4. [Jolley eq 238]

Sum_{n>=0} 4/a(n) = (Pi-2)/4. [Jolley, eq. 238]

From _Sum_{n>=0} (-1)^n/a(n) = 1/8 + (log(2*sqrt(2)+3) - Pi)/(16*sqrt(2)). - _Amiram Eldar_, Feb 27 2022: (Start)

Sum_{n>=0} 1/a(n) = (Pi-2)/16.

Sum_{n>=0} (-1)^n/a(n) = 1/8 + (log(2*sqrt(2)+3) - Pi)/(16*sqrt(2)). (End)

#19 by Amiram Eldar at Sun Feb 27 01:51:38 EST 2022

FORMULA

From Amiram Eldar, Feb 27 2022: (Start)

Sum_{n>=0} 1/a(n) = (Pi-2)/16.

Sum_{n>=0} (-1)^n/a(n) = 1/8 + (log(2*sqrt(2)+3) - Pi)/(16*sqrt(2)). (End)

STATUS

approved

editing

#18 by Charles R Greathouse IV at Fri Oct 16 14:56:03 EDT 2015

STATUS

editing

approved

#17 by Charles R Greathouse IV at Fri Oct 16 14:55:30 EDT 2015

FORMULA

a(0)=15, a(1)=315, a(2)=1287, a(3)=3315; for n>3, a(n) = 4*a(n-1)-6*a(n-2)+ 4*a(n-3)- a(n-4). [_). - _Harvey P. Dale_, May 06 2012]

PROG

(PARI) a(n)=(4*n+1)*(4*n+3)*(4*n+5) \\ Charles R Greathouse IV, Oct 16 2015

STATUS

approved

editing

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Last modified August 18 11:36 EDT 2024. Contains 375266 sequences. (Running on oeis4.)