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 A247907 Expansion of (1 + x) / ((1 - x^4) * (1 - x - x^5)) in powers of x. 3
 1, 2, 2, 2, 3, 5, 7, 9, 12, 16, 21, 28, 38, 51, 67, 88, 117, 156, 207, 274, 363, 481, 637, 844, 1119, 1483, 1964, 2601, 3446, 4566, 6049, 8013, 10615, 14062, 18628, 24677, 32691, 43307, 57369, 75997, 100675, 133367, 176674, 234043, 310041, 410717, 544084 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1,1,-1,1,-1). FORMULA G.f.: 1 / ((1 - x) * (1 - x + x^2) * (1 + x^2) * (1 - x^2 - x^3)). a(n) = -A247918(-8-n) for all n in Z. Convolution of A003520 and A133872. 0 = a(n) + a(n+4) - a(n+5) + mod(floor((n-1) / 2), 2) for all n in Z. 0 = a(n) - a(n+1) + a(n+2) - a(n+3) + a(n+4) - 2*a(n+5) + 2*a(n+6) - 2*a(n+7) + a(n+8) for all n in Z. EXAMPLE G.f. = 1 + 2*x + 2*x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 7*x^6 + 9*x^7 + 12*x^8 + ... MATHEMATICA CoefficientList[Series[(1 + x)/((1 - x^4) (1 - x - x^5)), {x, 0, 100}], x] (* Vincenzo Librandi, Sep 27 2014 *) PROG (PARI) {a(n) = if( n<0, n=-8-n; polcoeff( -1 / ((1 - x) * (1 - x + x^2) * (1 + x^2) * (1 + x - x^3)) + x * O(x^n), n), polcoeff( 1 / ((1 - x) * (1 - x + x^2) * (1 + x^2) * (1 - x^2 - x^3)) + x * O(x^n), n))}; (Magma) m:=60; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 +x)/((1-x^4)*(1-x-x^5)))); // G. C. Greubel, Aug 04 2018 CROSSREFS Cf. A003520, A133872, A247918. Sequence in context: A126111 A100142 A296103 * A122789 A291294 A014208 Adjacent sequences: A247904 A247905 A247906 * A247908 A247909 A247910 KEYWORD nonn,easy AUTHOR Michael Somos, Sep 26 2014 STATUS approved

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Last modified December 5 05:37 EST 2023. Contains 367575 sequences. (Running on oeis4.)