|
Search: id:A131865
|
|
|
| A131865 |
|
Partial sums of powers of 16. |
|
+0
7
|
|
| 1, 17, 273, 4369, 69905, 1118481, 17895697, 286331153, 4581298449, 73300775185, 1172812402961, 18764998447377, 300239975158033, 4803839602528529, 76861433640456465, 1229782938247303441, 19676527011956855057
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
a(n) = if n=0 then 1 else a(n-1)+A001025(n);
for n>0: A131851(a(n))=n and ABS(A131851(m))<n for m<a(n);
a(n) = A098704(n+2)/2.
16=2^4 is the growth measure for the Jacobsthal spiral (compare with phi^4 for the Fibonacci spiral). - Paul Barry (pbarry(AT)wit.ie), Mar 07 2008
Bisection of A115451. - Paul Curtz (bpcrtz(AT)free.fr), May 20 2008
Second quadrisection of A115451. - Paul Curtz (bpcrtz(AT)free.fr), May 21 2008
|
|
FORMULA
|
a(n) = (A001025(n+1)-1)/15.
a(n)=16a(n-1)+1. - Paul Curtz (bpcrtz(AT)free.fr), May 20 2008
a(n)=16a(n-1)+1. - Paul Curtz (bpcrtz(AT)free.fr), May 21 2008
|
|
EXAMPLE
|
a(3) = 1+16+256+4096 = 4369 = in binary: 1000100010001.
|
|
MATHEMATICA
|
Table[(2^(4 n) - 1)/15, {n, 16}] (* Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 22 2007 *)
|
|
PROGRAM
|
(Other) sage: [gaussian_binomial(n, 1, 16) for n in xrange(1, 18)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
|
|
CROSSREFS
|
Cf. A000225, A002450, A023001, A132469.
Sequence in context: A142898 A159678 A097830 this_sequence A031417 A029811 A113076
Adjacent sequences: A131862 A131863 A131864 this_sequence A131866 A131867 A131868
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 22 2007
|
|
|
Search completed in 0.002 seconds
|
