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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 Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Alice V. Kleeva, Grid for this sequence Alice V. Kleeva, Illustration of initial terms Robert Munafo, Sequence A169720, and two others by Alice V. Kleeva Robert Munafo, Sequence A169720, and two others by Alice V. Kleeva [Cached copy, in pdf format, included with permission] Index entries for linear recurrences with constant coefficients, signature (7,-14,8). - R. J. Mathar, Apr 26 2010 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 Cf. A000079, A003215, A169720-A169727. Sequence in context: A049494 A049495 A169789 * A305781 A172063 A208737 Adjacent sequences: A169723 A169724 A169725 * A169727 A169728 A169729 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.)