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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
Alice V. Kleeva, Grid for this sequence
Robert Munafo, Sequence A169720, and two others by Alice V. Kleeva [Cached copy, in pdf format, included with permission]
FORMULA
From R. J. Mathar, Apr 26 2010:
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)
a(n) = (2*A169720(n)+1)/3. - L. Edson Jeffery, Dec 03 2012
MAPLE
A169726:=n->3*2^n*(2^n-1)+1: seq(A169726(n), n=0..30); # Wesley Ivan Hurt, Sep 14 2014
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
(Magma) [3*2^n*(2^n-1)+1 : n in [0..30]]; // Wesley Ivan Hurt, Sep 14 2014
CROSSREFS
Sequence in context: A049494 A049495 A169789 * A305781 A172063 A208737
KEYWORD
nonn,easy
AUTHOR
Alice V. Kleeva (alice27353(AT)gmail.com), Jan 19 2010
STATUS
approved

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Last modified February 24 20:15 EST 2024. Contains 370307 sequences. (Running on oeis4.)