A129346 a(2n) = A100525(n), a(2n+1) = A001653(n+1); a Pellian-related sequence.

4, 5, 22, 29, 128, 169, 746, 985, 4348, 5741, 25342, 33461, 147704, 195025, 860882, 1136689, 5017588, 6625109, 29244646, 38613965, 170450288, 225058681, 993457082, 1311738121, 5790292204, 7645370045, 33748296142, 44560482149, 196699484648, 259717522849

Offset

0,1

Comments

Summation of -a(n) and A129345 returns twice Pell numbers A000129 (apart from signs; starting from 2nd term of A000129).

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,6,0,-1).

Formula

O.g.f.: (4 + 5*x - 2*x^2 - x^3) / ((x^2 - 2*x - 1)*(x^2 + 2*x - 1)).

From Colin Barker, May 26 2016: (Start)

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

a(n) = 6*a(n-2)-a(n-4) for n>3. (End)

E.g.f.: 2*cosh(sqrt(2)*x)*(sinh(x) + 2*cosh(x)) + (sinh(sqrt(2)*x)*(5*sinh(x) + 3*cosh(x)))/sqrt(2). - Ilya Gutkovskiy, May 26 2016

Mathematica

LinearRecurrence[{0, 6, 0, -1}, {4, 5, 22, 29}, 30] (* Harvey P. Dale, Apr 08 2018 *)

Prog

(PARI) Vec((4+5*x-2*x^2-x^3)/((x^2-2*x-1)*(x^2+2*x-1)) + O(x^40)) \\ Colin Barker, May 26 2016

Crossrefs

Cf. A129345, A000129, A001542, A038761.

Sequence in context: A284911 A091130 A141447 * A291670 A176957 A341586

Adjacent sequences: A129343 A129344 A129345 * A129347 A129348 A129349

Keyword

nonn,easy

Author

Creighton Dement, Apr 10 2007

Status

approved