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 A097178 Expansion of (1+10*x-101*x^2-900*x^3)/((1-100*x^2)*(1-101*x^2)). 2
 1, 10, 100, 1110, 10000, 122110, 1000000, 13333110, 100000000, 1446644110, 10000000000, 156111055110, 1000000000000, 16767216566110, 100000000000000, 1793488873177110, 10000000000000000, 191142376190888110 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Partial sums are A097177. LINKS G. C. Greubel, Table of n, a(n) for n = 0..980 Index entries for linear recurrences with constant coefficients, signature (0,201,0,-10100). FORMULA a(n) = (55/sqrt(101))*( (sqrt(101))^n - (-sqrt(101))^n ) + 10^n * (11*(-1)^n-9)/2. a(n) = 201*a(n-2) - 10100*a(n-4). MAPLE seq(coeff(series((1+10*x-101*x^2-900*x^3)/((1-100*x^2)*(1-101*x^2)), x, n+1), x, n), n = 0 ..20); # G. C. Greubel, Sep 17 2019 MATHEMATICA CoefficientList[Series[(1+10x-101x^2-900x^3)/((1-100x^2)(1-101x^2)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jan 13 2017 *) LinearRecurrence[{0, 201, 0, -10100}, {1, 10, 100, 1110}, 20] (* Harvey P. Dale, Mar 03 2018 *) PROG (PARI) my(x='x+O('x^20)); Vec((1+10*x-101*x^2-900*x^3)/((1-100*x^2)*(1-101*x^2))) \\ G. C. Greubel, Sep 17 2019 (Magma) R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+10*x-101*x^2-900*x^3)/((1-100*x^2)*(1-101*x^2)) )); // G. C. Greubel, Sep 17 2019 (Sage) def A097178_list(prec): P. = PowerSeriesRing(ZZ, prec) return P((1+10*x-101*x^2-900*x^3)/((1-100*x^2)*(1-101*x^2))).list() A097178_list(20) # G. C. Greubel, Sep 17 2019 (GAP) a:=[1, 10, 100, 1110];; for n in [5..20] do a[n]:=201*a[n-2] - 10100*a[n-4]; od; a; # G. C. Greubel, Sep 17 2019 CROSSREFS Sequence in context: A164832 A144822 A199763 * A283288 A283377 A283352 Adjacent sequences: A097175 A097176 A097177 * A097179 A097180 A097181 KEYWORD easy,nonn AUTHOR Paul Barry, Jul 30 2004 STATUS approved

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Last modified June 23 03:01 EDT 2024. Contains 373629 sequences. (Running on oeis4.)