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 A219721 Expansion of (1+7*x+5*x^2+7*x^3+x^4)/(1-x-x^4+x^5). 2
 1, 8, 13, 20, 22, 29, 34, 41, 43, 50, 55, 62, 64, 71, 76, 83, 85, 92, 97, 104, 106, 113, 118, 125, 127, 134, 139, 146, 148, 155, 160, 167, 169, 176, 181, 188, 190, 197, 202, 209, 211, 218, 223, 230, 232, 239, 244, 251, 253, 260, 265, 272, 274, 281, 286, 293 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Positive values of y in the Diophantine equation 21*x+1 = y^2; the corresponding values ​​of x are given in A219391. Equivalently, numbers that are congruent to {1,8,13,20} mod 21. The product of any two terms belongs to the sequence and therefore also a(n)^2, a(n)^3, a(n)^4 etc. LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1). FORMULA G.f.: (1+7*x+5*x^2+7*x^3+x^4)/((1+x)*(1-x)^2*(1+x^2)). a(n) = -a(-n-1) = (42*n-6*i^(n*(n-1))-7*(-1)^n+5)/8 +2, where i=sqrt(-1). MATHEMATICA CoefficientList[Series[(1 + 7 x + 5 x^2 + 7 x^3 + x^4)/(1 - x - x^4 + x^5), {x, 0, 60}], x] LinearRecurrence[{1, 0, 0, 1, -1}, {1, 8, 13, 20, 22}, 60] (* Vincenzo Librandi, Aug 18 2013 *) PROG (PARI) Vec((1+7*x+5*x^2+7*x^3+x^4)/(1-x-x^4+x^5)+O(x^60)) (Maxima) makelist(coeff(taylor((1+7*x+5*x^2+7*x^3+x^4)/(1-x-x^4+x^5), x, 0, n), x, n), n, 0, 60); (Magma) I:=[1, 8, 13, 20, 22]; [n le 5 select I[n] else Self(n-1) +Self(n-4)-Self(n-5): n in [1..60]]; // Vincenzo Librandi, Aug 18 2013 CROSSREFS Cf. A219391. Sequence in context: A070130 A070131 A030782 * A176209 A227453 A266212 Adjacent sequences: A219718 A219719 A219720 * A219722 A219723 A219724 KEYWORD nonn,easy AUTHOR Bruno Berselli, Nov 26 2012 STATUS approved

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Last modified January 28 08:35 EST 2023. Contains 359850 sequences. (Running on oeis4.)