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A169720 (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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A subsequence of the triangular numbers A000217.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..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 - From N. J. A. Sloane, Dec 05 2012

Index to sequences with 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

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: A249460 A022575 A202481 * A024210 A188168 A199413

Adjacent sequences:  A169717 A169718 A169719 * A169721 A169722 A169723

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified December 22 14:10 EST 2014. Contains 252364 sequences.