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 A110293 a(2*n) = A001570(n), a(2*n+1) = A011943(n+1). 3
 1, 7, 13, 97, 181, 1351, 2521, 18817, 35113, 262087, 489061, 3650401, 6811741, 50843527, 94875313, 708158977, 1321442641, 9863382151, 18405321661, 137379191137, 256353060613, 1913445293767, 3570537526921, 26650854921601, 49731172316281, 371198523608647 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS See also A110294 (compare program code). a(2*n+1) = (a(2*n) + a(2*n+2))/2 and see A232765 for Diophantine equation that produces a sequence related to a(n). - Richard R. Forberg, Nov 30 2013 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,14,0,-1). FORMULA G.f.: (1+7*x-x^2-x^3) / ((x^2-4*x+1)*(x^2+4*x+1)). From Colin Barker, Nov 01 2016: (Start) a(n) = ((-1)*((-3+(-1)^n)*((2-sqrt(3))^n*(-3+2*sqrt(3))+(2+sqrt(3))^n*(3+2*sqrt(3)))))/(8*sqrt(3)). a(n) = 14*a(n-2)-a(n-4) for n>3. (End) MAPLE seriestolist(series((1+7*x-x^2-x^3)/((x^2-4*x+1)*(x^2+4*x+1)), x=0, 25)); # -or- Floretion Algebra Multiplication Program, FAMP Code: 1leszapseq[A*B] with A = - 'j + 'k - j' + k' - 'ii' - 'ij' - 'ik' - 'ji' - 'ki' and B = + .5'ij' + .5'ji' MATHEMATICA CoefficientList[Series[(1 + 7 x - x^2 - x^3)/((x^2 - 4 x + 1) (x^2 + 4 x + 1)), {x, 0, 25}], x] (* Michael De Vlieger, Nov 01 2016 *) PROG (PARI) Vec((1+7*x-x^2-x^3)/((1-4*x+x^2)*(1+4*x+x^2)) + O(x^30)) \\ Colin Barker, Nov 01 2016 CROSSREFS Cf. A001570, A011943, A110294, A232765 Sequence in context: A110455 A177952 A132373 * A253333 A039687 A001544 Adjacent sequences:  A110290 A110291 A110292 * A110294 A110295 A110296 KEYWORD easy,nonn AUTHOR Creighton Dement, Jul 18 2005 STATUS approved

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