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URL: https://oeis.org/A129346

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A129346
a(2n) = A100525(n), a(2n+1) = A001653(n+1); a Pellian-related sequence.
2
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).
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
KEYWORD
nonn,easy
AUTHOR
Creighton Dement, Apr 10 2007
STATUS
approved