|
Search: id:A140065
|
|
|
| A140065 |
|
Binomial transform of [1, 2, 7, 0, 0, 0,...]. |
|
+0
1
|
|
| 1, 3, 12, 28, 51, 81, 118, 162, 213, 271, 336, 408, 487, 573, 666, 766, 873, 987, 1108, 1236, 1371, 1513, 1662, 1818, 1981, 2151, 2328, 2512, 2703, 2901, 3106, 3318, 3537, 3763, 3996, 4236, 4483, 4737, 4998, 5266, 5541, 5823, 6112, 6408, 6711, 7021, 7338
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
FORMULA
|
A007318 * [1, 2, 7, 0, 0, 0,...]
a(n) = A000217(n)+6*A000217(n-2) = (A140064(n)+A140066(n))/2. O.g.f.: x*(1+6x^2)/(1-x)^3. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 06 2008
a(n)=(12-17n+7n^2)/2. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 07 2008
Ogf([1,3,12,28,51,81,118,162,213,271,336,408,487,573]) = (6*x^2 + 1)/(-x^3 + 3*x^2 - 3*x + 1) - Alexander R. Povolotsky (pevnev(AT)juno.com), May 06 2008
a(n)=7*n+a(n-1)-12 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]
|
|
EXAMPLE
|
a(4) = 28 = (1, 3, 3, 1) dot (1, 2, 7, 0) = (1 + 6 + 21 + 0).
For n=2, a(2)=7*2+1-12=3; n=3, a(3)=7*3+3-12=12; n=4, a(4)=7*4+12-12=28 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 09 2009]
|
|
MAPLE
|
seq((12-17*n+7*n^2)*1/2, n=1..40); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 07 2008
|
|
MATHEMATICA
|
s=1; lst={s}; Do[s+=n+1; AppendTo[lst, s], {n, 1, 6!, 7}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]
|
|
CROSSREFS
|
Sequence in context: A060781 A083539 A066643 this_sequence A115549 A005995 A034503
Adjacent sequences: A140062 A140063 A140064 this_sequence A140066 A140067 A140068
|
|
KEYWORD
|
nonn,new
|
|
AUTHOR
|
Gary W. Adamson (qntmpkt(AT)yahoo.com), May 03 2008
|
|
EXTENSIONS
|
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Emeric Deutsch (deutsch(AT)duke.poly.edu), May 06 2008
More terms and Mathematica program Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008
|
|
|
Search completed in 0.002 seconds
|
