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A206373 (14*4^n + 1)/3. 0
5, 19, 75, 299, 1195, 4779, 19115, 76459, 305835, 1223339, 4893355, 19573419, 78293675, 313174699, 1252698795, 5010795179, 20043180715, 80172722859, 320690891435, 1282763565739, 5131054262955, 20524217051819, 82096868207275, 328387472829099, 1313549891316395 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A generalized Engel expansion of 2/7 to the base b := 4/3 as defined in A181565 with associated series expansion 2/7 = b/5 + b^2/(5*19) + b^3/(5*19*75) + b^4/(5*19*75*299) + .... - Peter Bala, Oct 30 2013

LINKS

Table of n, a(n) for n=0..24.

FORMULA

a(n) = (14*4^n +1)/3.

From Peter Bala, Oct 30 2013: (Start)

Recurrence equations:

a(n+1) = 4*a(n) - 1 with a(0) = 5.

a(n) = 5*a(n-1) - 4*a(n-2) with a(0) = 5 and a(1) = 19.

O.g.f. (5 - 6*x)/((1 - x)*(1 - 4*x)) = 5 + 19*x + 75*x^2 + .... (End)

PROG

(MAGMA) [(14*4^n+1)/3 : n in [0..30]];

(PARI) a(n)=(14*4^n + 1)/3 \\ Charles R Greathouse IV, Jun 01 2015

CROSSREFS

Cf. A181565.

Sequence in context: A212403 A098913 A126392 * A149767 A149768 A149769

Adjacent sequences:  A206370 A206371 A206372 * A206374 A206375 A206376

KEYWORD

nonn,easy

AUTHOR

Brad Clardy, Feb 07 2012

STATUS

approved

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Last modified October 18 07:00 EDT 2018. Contains 316307 sequences. (Running on oeis4.)