|
|
A169726
|
|
a(n) = 3*2^n*(2^n-1) + 1.
|
|
3
|
|
|
1, 7, 37, 169, 721, 2977, 12097, 48769, 195841, 784897, 3142657, 12576769, 50319361, 201302017, 805257217, 3221127169, 12884705281, 51539214337, 206157643777, 824632147969, 3298531737601, 13194133241857, 52776545550337, 211106207367169, 844424879800321
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
A subsequence of the centered hexagonal numbers A003215.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3).
G.f.: ( -1-2*x^2 ) / ( (x-1)*(2*x-1)*(4*x-1) ). (End)
|
|
MAPLE
|
|
|
MATHEMATICA
|
CoefficientList[Series[(-1 - 2*x^2)/((x-1)*(2*x-1)*(4*x-1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 04 2012 *)
Table[c=2^n; 3c(c-1)+1, {n, 0, 30}] (* or *) LinearRecurrence[{7, -14, 8}, {1, 7, 37}, 30] (* Harvey P. Dale, Nov 22 2013 *)
|
|
PROG
|
(Magma) I:=[1, 7, 37]; [n le 3 select I[n] else 7*Self(n-1) -14*Self(n-2) +8*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Dec 04 2012
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Alice V. Kleeva (alice27353(AT)gmail.com), Jan 19 2010
|
|
STATUS
|
approved
|
|
|
|