login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A034478 (5^n+1)/2. 15
1, 3, 13, 63, 313, 1563, 7813, 39063, 195313, 976563, 4882813, 24414063, 122070313, 610351563, 3051757813, 15258789063, 76293945313, 381469726563, 1907348632813, 9536743164063, 47683715820313, 238418579101563 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Terms are also the quotients arising from sequence A050621.

Binomial transform of A081294. - Paul Barry, Jan 13 2005

a(n)^2 + (a(n) - 1)^2 = a(2*n). E.g., 63^2 + 62^2 = 7813 = a(6). - Gary W. Adamson, Jun 17 2006

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..250

FORMULA

E.g.f.: exp(3*x)*cosh(2*x). - Paul Barry, Mar 17 2003

Partial sums of A020699. G.f.: (1-3*x)/((1-x)*(1-5*x)). - Paul Barry, Sep 03 2003

a(n)=sum{k=0..n, sum{j=0..k, C(n, k)*C(2*k, 2*j)}} - Paul Barry, Jan 13 2005

a(n) = 6*a(n-1) - 5*a(n-2), a(0) = 1, a(1) = 3. - Philippe Deléham, Jul 11 2005

a(n)=5*a(n-1)-2 with a(0)=1. - Vincenzo Librandi, Aug 01 2010

EXAMPLE

For n=1, a(1)=5*1-2=3; n=2, a(2)=5*3-2=13; n=3, a(3)=5*13-2=63. - Vincenzo Librandi, Aug 01 2010

G.f. = 1 + 3*x + 13*x^2 + 63*x^3 + 313*x^4 + 1563*x^5 + 7813*x^6 + ...

MAPLE

seq((5^n + 1)/2, n=0..20); # Zerinvary Lajos, Jun 16 2007

PROG

(Sage) [lucas_number2(n, 6, 5)/2 for n in xrange(0, 22)] # Zerinvary Lajos, Jul 08 2008

CROSSREFS

Cf. A050621.

Sequence in context: A276893 A284160 A092467 * A026715 A001850 A130525

Adjacent sequences:  A034475 A034476 A034477 * A034479 A034480 A034481

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 21 02:19 EST 2018. Contains 299388 sequences. (Running on oeis4.)