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 A092534 Expansion of (1-x+x^2)*(1+x^4)/((1-x)^2*(1-x^2)). 1
 1, 1, 3, 4, 8, 10, 16, 20, 28, 34, 44, 52, 64, 74, 88, 100, 116, 130, 148, 164, 184, 202, 224, 244, 268, 290, 316, 340, 368, 394, 424, 452, 484, 514, 548, 580, 616, 650, 688, 724, 764, 802, 844, 884, 928, 970, 1016, 1060, 1108, 1154, 1204, 1252, 1304, 1354, 1408, 1460 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS At one time this was given as the g.f. for A004657. In fact it produces a different sequence, showm here. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,1). Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1). FORMULA The g.f. can also be written as (1+x^2+x^4)*(1+x^4)/((1-x)*(1-x^2)*(1-x^3)). - N. J. A. Sloane, Nov 07 2017 From Colin Barker, Apr 14 2016: (Start) a(n) = (13+3*(-1)^n-4*n+2*n^2)/4 for n>2. a(n) = (n^2-2*n+8)/2 for n>2 and even. a(n) = (n^2-2*n+5)/2 for n>2 and odd. a(n) = a(n-1)+a(n-2)-a(n-4)-a(n-5)+a(n-6) for n>6. (End) MATHEMATICA CoefficientList[Series[(1+x^2+x^4)(1+x^4)/((1-x)(1-x^2)(1-x^3)), {x, 0, 60}], x] (* or *) LinearRecurrence[{2, 0, -2, 1}, {1, 1, 3, 4, 8, 10, 16}, 60] (* Harvey P. Dale, Nov 07 2017 *) PROG (PARI) Vec((1+x^2+x^4)*(1+x^4)/((1-x)*(1-x^2)*(1-x^3)) + O(x^50)) \\ Colin Barker, Apr 14 2016 CROSSREFS Sequence in context: A026494 A043306 A131355 * A005232 A165272 A310010 Adjacent sequences:  A092531 A092532 A092533 * A092535 A092536 A092537 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Apr 08 2004 EXTENSIONS Definition simplified by N. J. A. Sloane, Nov 07 2017 STATUS approved

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Last modified June 25 14:43 EDT 2019. Contains 324352 sequences. (Running on oeis4.)