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URL: https://oeis.org/A169720

⇱ A169720 - OEIS

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A169720
a(n) = (3*2^(n-1)-1)*(3*2^n-1).
8
1, 10, 55, 253, 1081, 4465, 18145, 73153, 293761, 1177345, 4713985, 18865153, 75479041, 301953025, 1207885825, 4831690753, 19327057921, 77308821505, 309236465665, 1236948221953, 4947797606401, 19791199862785, 79164818325505, 316659311050753, 1266637319700481
OFFSET
0,2
COMMENTS
A subsequence of the triangular numbers A000217.
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
G.f.: (1 + 3*x - x^2)/((1-x)*(1-2*x)*(1-4*x)). - Paul D. Hanna, Apr 29 2010
a(n) = A000217(A033484(n)). - Mitch Harris, Dec 02 2012
a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3). - Vincenzo Librandi, Dec 03 2012
a(n) = (3*A169726(n)-1)/2. - L. Edson Jeffery, Dec 03 2012
a(n) = A006095(n+2) +3*A006095(n+1) - A006905(n). - R. J. Mathar, Dec 04 2016
MATHEMATICA
CoefficientList[Series[(1 + 3*x - x^2)/((1-x)*(1-2*x)*(1-4*x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{7, -14, 8}, {1, 10, 55}, 30] (* Vincenzo Librandi, Dec 03 2012 *)
PROG
(PARI) a(n)=polcoeff((1+3*x-x^2)/((1-x)*(1-2*x)*(1-4*x)+x*O(x^n)), n) \\ Paul D. Hanna, Apr 29 2010
(Magma) I:=[1, 10, 55]; [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 03 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alice V. Kleeva (alice27353(AT)gmail.com), Jan 19 2010
STATUS
approved