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A080960 Third binomial transform of A010685 (period 2: repeat 1,4). 5
1, 7, 34, 148, 616, 2512, 10144, 40768, 163456, 654592, 2619904, 10482688, 41936896, 167759872, 671064064, 2684305408, 10737319936, 42949476352, 171798298624, 687193980928, 2748777496576, 10995113132032, 43980458819584 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (6,-8).

FORMULA

a(n) = 4*a(n-1)+3*2^(n-1).

a(n) = (5/2)*4^n-(3/2)*2^n.

G.f.: (1+x)/((1-2*x)*(1-4*x)). [Klaus Brockhaus, Nov 26 2009]

a(0)=1, a(1)=7, a(n)=6*a(n-1)-8*a(n-2). - Harvey P. Dale, Nov 12 2012

MATHEMATICA

RecurrenceTable[{a[0]==1, a[n]==4a[n-1]+3*2^(n-1)}, a, {n, 30}] (* or *) LinearRecurrence[{6, -8}, {1, 7}, 30] (* Harvey P. Dale, Nov 12 2012 *)

CoefficientList[Series[(1 + x) / ((1 - 2 x) (1 - 4 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)

PROG

(MAGMA) binomtf:=func< V | [ &+[ Binomial(i-1, k-1)*V[k]: k in [1..i] ]: i in [1..#V] ] >; binomtf(binomtf(binomtf(&cat[ [1, 4]: n in [1..12] ]))); // Klaus Brockhaus, Nov 26 2009

CROSSREFS

Cf. A010685, A080961, A048473, A003945.

Sequence in context: A306376 A192803 A052161 * A243414 A213119 A099242

Adjacent sequences:  A080957 A080958 A080959 * A080961 A080962 A080963

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 03 2003

EXTENSIONS

Definition corrected, edited by Klaus Brockhaus, Nov 26 2009

STATUS

approved

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Last modified June 26 00:41 EDT 2019. Contains 324367 sequences. (Running on oeis4.)