A169720 a(n) = (3*2^(n-1)-1)*(3*2^n-1).

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

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).

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

Cf. A169721-A169727, A033484, A000217.

Sequence in context: A022575 A202481 A348663 * A024210 A253002 A357668

Adjacent sequences: A169717 A169718 A169719 * A169721 A169722 A169723

Keyword

nonn,easy

Author

Alice V. Kleeva (alice27353(AT)gmail.com), Jan 19 2010

Status

approved