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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A085781 a(n) = 2*binomial(2*n+1,n+1) - 2^n. 0
1, 4, 16, 62, 236, 892, 3368, 12742, 48364, 184244, 704408, 2702108, 10396504, 40108408, 155101136, 601047622, 2333540684, 9075004228, 35345001656, 137846004532, 538256825864, 2104096866568, 8233426533296, 32247595294492 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Create a triangle with the first column being the n-th row of Pascal's triangle from A007318, T(r,0) = binomial(n,r). The other terms T(r,c) are defined as T(r,c-1) + T(r-1,c-1). The sum of all terms for each triangle having n+1 rows is a(n). Example for n=3: the triangle has four rows 1; 3,4; 3,6,10; 1,4,10,20 ; sum of all 10 elements in the triangle is 62=a(3). - J. M. Bergot, Jan 17 2013

LINKS

Table of n, a(n) for n=0..23.

FORMULA

a(n) = sum(sum(binomial(i,j), i=n..n+j), j=0..n) = 2*A001700(n)-A000079(n).

Conjecture: (n+1)*a(n) -2*(4*n+1)*a(n-1) +4*(5*n-3)*a(n-2) +8*(-2*n+3)*a(n-3)=0. - R. J. Mathar, Jan 25 2013

MAPLE

seq(2*binomial(2*n+1, n+1)-2^n, n=0..25);

CROSSREFS

Sequence in context: A084859 A081666 A250346 * A113438 A268429 A195339

Adjacent sequences:  A085778 A085779 A085780 * A085782 A085783 A085784

KEYWORD

nonn,easy

AUTHOR

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jul 23 2003

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 20 21:03 EST 2019. Contains 329348 sequences. (Running on oeis4.)