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A094706 Convolution of Pell(n) and 2^n. 6
0, 1, 4, 13, 38, 105, 280, 729, 1866, 4717, 11812, 29365, 72590, 178641, 438064, 1071153, 2613138, 6362965, 15470140, 37565389, 91125206, 220864377, 534951112, 1294960905, 3133261530, 7578261181, 18323338324, 44292046693, 107041649438 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = sum of n-th row in A101164 = A000129(n) - A000079(n). - Reinhard Zumkeller, Dec 03 2004

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

S. Falcon, On The Generating Functions of the Powers of the K-Fibonacci Numbers, Scholars Journal of Engineering and Technology (SJET), 2014; 2 (4C):669-675.

Index entries for linear recurrences with constant coefficients, signature (4,-3,-2).

FORMULA

G.f.: x/((1-2x-x^2)(1-2x)).

a(n) = Sum_{k=0..n} ((1+sqrt(2))^n - (1-sqrt(2))^n)/(2*sqrt(2))*2^(n-k).

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

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

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k+1)*2^(n-2k-1);

a(n) = Sum_{k=0..n} binomial(k, n-k+1)*2^k*(1/2)^(n-k+1). - Paul Barry, Oct 07 2004

a(n) = A000129(n+2) - 2^(n+1). - R. J. Mathar, Jan 29 2012

MATHEMATICA

LinearRecurrence[{4, -3, -2}, {0, 1, 4}, 40] (* Vincenzo Librandi, Jun 24 2012 *)

PROG

(MAGMA) I:=[0, 1, 4]; [n le 3 select I[n] else 4*Self(n-1)-3*Self(n-2)-2*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 24 2012

CROSSREFS

Cf. A000079, A000129.

Sequence in context: A181527 A049611 A084851 * A325927 A056014 A247287

Adjacent sequences:  A094703 A094704 A094705 * A094707 A094708 A094709

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 21 2004

STATUS

approved

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Last modified November 14 01:24 EST 2019. Contains 329108 sequences. (Running on oeis4.)