|
| |
|
|
A033114
|
|
Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,0.
|
|
6
| |
|
|
1, 4, 17, 68, 273, 1092, 4369, 17476, 69905, 279620, 1118481, 4473924, 17895697, 71582788, 286331153, 1145324612, 4581298449, 18325193796, 73300775185, 293203100740, 1172812402961, 4691249611844, 18764998447377, 75059993789508
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Partial sums of A015521 [From Mircea Merca, Dec 28 2010]
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for sequences related to linear recurrences with constant coefficients, signature (4,1,-4).
|
|
|
FORMULA
| a(n) = floor(4^(n+1)/15) = 4^(n+1)/15-1/6-(-1)^n/10. - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 18 2003
G.f.: 1/((1-x)*(1+x)*(1-4*x)); a(n)=3*a(n-1)+4*a(n-2)+1. Partial sum of A015521. - Paul Barry (pbarry(AT)wit.ie), Nov 12 2003
a(n)=sum{k=0..floor(n/2), 4^(n-2*k) }; a(n)=sum{k=0..n, sum{j=0..k, (-1)^(j+k)*4^j }}. - Paul Barry (pbarry(AT)wit.ie), Nov 12 2003
Convolution of A000302 and A059841 (4^n and periodic{1, 0}). a(n)=sum{k=0..n, (1+(-1)^(n-k))*4^k/2 } - Paul Barry (pbarry(AT)wit.ie), Jul 19 2004
a(n)=sum{k=0..n, (-1)^(n-k)*(J(2*k+1)-1)/2}, J(n)=A001045(n); - Paul Barry (pbarry(AT)wit.ie), Mar 06 2008
a(n)=round((8*4^n-5)/30)=floor((4*4^n-1)/15)=ceil((4*4^n-4)/15)=round((4*4^n-4)/15); a(n)=a(n-2)+4^(n-1), n>1. [From Mircea Merca, Dec 28 2010]
|
|
|
MAPLE
| seq(floor((4^(n+1)-1)/15), n=1..25) [From Mircea Merca, Dec 28 2010]
|
|
|
MATHEMATICA
| Join[{a=1, b=4}, Table[c=3*b+4*a+1; a=b; b=c, {n, 100}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 17 2011*)
|
|
|
PROG
| (MAGMA) [Round((8*4^n-5)/30): n in [1..30]]; // Vincenzo Librandi, Jun 25 2011
|
|
|
CROSSREFS
| Cf. A015521
Sequence in context: A030529 A081113 A114587 * A096881 A033122 A005511
Adjacent sequences: A033111 A033112 A033113 * A033115 A033116 A033117
|
|
|
KEYWORD
| nonn,base,easy
|
|
|
AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
|
| |
|
|
