The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A053141 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A053141

a(0)=0, a(1)=2 then a(n) = a(n-2) + 2*sqrt(8*a(n-1)^2 + 8*a(n-1) + 1).
(history; published version)

#176 by Michael De Vlieger at Thu Sep 12 07:49:11 EDT 2024

STATUS

reviewed

approved

#175 by Joerg Arndt at Thu Sep 12 03:34:51 EDT 2024

STATUS

proposed

reviewed

#174 by Pontus von Brömssen at Wed Sep 11 07:51:45 EDT 2024

STATUS

editing

proposed

#173 by Pontus von Brömssen at Wed Sep 11 07:22:20 EDT 2024

COMMENTS

Jason Holt observes that a pair drawn from a drawer with A053141(n)+1 red socks and A001652(n) - A053141(n) blue socks will as likely as not be matching reds: (A053141+1)*A053141/((A001652+1)*A001652 ) = 1/2, n>0. - Bill Gosper, Feb 07 2010

FORMULA

a(n) = (A001653(n)-1)/2 = 2*A053142(n) = A011900(n)-1). [Corrected by _Pontus von Brömssen_, Sep 11 2024]

a(n) = A000194(A029549(n)) = A002024(A075528(n)). - Pontus von Brömssen, Sep 11 2024

CROSSREFS

Cf. A000194, A001541, A002024, A016278, A046090, A055997, A077259, A077288, A077398, A084068.

STATUS

approved

editing

#172 by Michael De Vlieger at Sat Mar 16 15:22:10 EDT 2024

STATUS

reviewed

approved

#171 by Michel Marcus at Sat Mar 16 13:36:23 EDT 2024

STATUS

proposed

reviewed

#170 by Stefano Spezia at Sat Mar 16 12:16:54 EDT 2024

STATUS

editing

proposed

#169 by Stefano Spezia at Sat Mar 16 12:04:14 EDT 2024

FORMULA

E.g.f.: (exp(3*x)*(2*cosh(2*sqrt(2)*x) + sqrt(2)*sinh(2*sqrt(2)*x)) - 2*exp(x))/4. - Stefano Spezia, Mar 16 2024

STATUS

approved

editing

#168 by Alois P. Heinz at Fri Dec 08 09:40:31 EST 2023

STATUS

editing

approved

#167 by Alois P. Heinz at Fri Dec 08 09:40:27 EST 2023

DATA

0, 2, 14, 84, 492, 2870, 16730, 97512, 568344, 3312554, 19306982, 112529340, 655869060, 3822685022, 22280241074, 129858761424, 756872327472, 4411375203410, 25711378892990, 149856898154532, 873430010034204, 5090723162050694, 29670908962269962, 172934730611569080

STATUS

approved

editing