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A096881 Expansion of (1+4*x)/(1-17*x^2). 2
1, 4, 17, 68, 289, 1156, 4913, 19652, 83521, 334084, 1419857, 5679428, 24137569, 96550276, 410338673, 1641354692, 6975757441, 27903029764, 118587876497, 474351505988, 2015993900449, 8063975601796, 34271896307633 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (0,17).

FORMULA

a(n) = 3*a(n-1) + 4*a(n-2) + 17^floor((n-2)/2).

a(n) = sum{k=0..floor(n/2), binomial(floor(n/2), k)4^(n-2k) }.

a(n) = (1/5)*(-1)^n*Sum_{a=2..n}{17^floor(-1+1/2*a)*(-1)^a}+(4/5)*Sum_{a=2..n}{17^floor(-1+1/2*a) *(1/4)^a}*4^n+4^n, with n>=0. - Paolo P. Lava, Jun 12 2008

a(n) = 17*a(n-2), n>1. [Harvey P. Dale, Jan 21 2012]

MATHEMATICA

CoefficientList[Series[(1+4x)/(1-17x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[ {0, 17}, {1, 4}, 30] (* Harvey P. Dale, Jan 21 2012 *)

PROG

(PARI) Vec((1+4*x)/(1-17*x^2) + O(x^40)) \\ Michel Marcus, Jan 26 2016

(MAGMA) I:=[1, 4, 17]; [n le 3 select I[n] else 17*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jan 26 2016

CROSSREFS

Cf. A004663, A026383, A016116.

Sequence in context: A114587 A268431 A033114 * A344217 A033122 A330246

Adjacent sequences:  A096878 A096879 A096880 * A096882 A096883 A096884

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 14 2004

STATUS

approved

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Last modified September 28 19:16 EDT 2021. Contains 347717 sequences. (Running on oeis4.)