A080960 Third binomial transform of A010685 (period 2: repeat 1,4).

1, 7, 34, 148, 616, 2512, 10144, 40768, 163456, 654592, 2619904, 10482688, 41936896, 167759872, 671064064, 2684305408, 10737319936, 42949476352, 171798298624, 687193980928, 2748777496576, 10995113132032, 43980458819584

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

E.g.f.: exp(2*x)*(5*exp(2*x) - 3)/2. - G. C. Greubel, Nov 23 2021

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)/((1-2x)(1-4x)), {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
(Sage) [2^(n-1)*(5*2^n -3) for n in (0..30)] # G. C. Greubel, Nov 23 2021

Crossrefs

Cf. A003945, A010685, A048473, A080961.

Sequence in context: A306376 A192803 A052161 * A243414 A335087 A213119

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