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 A225883 a(n) = (-1)^n * (1 - 2^n). 3
 0, 1, -3, 7, -15, 31, -63, 127, -255, 511, -1023, 2047, -4095, 8191, -16383, 32767, -65535, 131071, -262143, 524287, -1048575, 2097151, -4194303, 8388607, -16777215, 33554431, -67108863, 134217727, -268435455, 536870911, -1073741823, 2147483647, -4294967295 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A001047(n) = p(0) where p(x) is the unique degree-(n-1) polynomial such that p(k) = a(k) for k = 1, 2, ..., n. a(n) = p(n) where p(x) is the unique degree-(n-1) polynomial such that p(k) = (-1)^k for k = 0, 1, ..., n-1. LINKS G. C. Greubel, Table of n, a(n) for n = 0..2500 Index entries for linear recurrences with constant coefficients, signature (-3, -2). FORMULA G.f.: x / ((1 + x) * (1 + 2*x)) = 1 / (1+x) - 1 / (1 + 2*x). E.g.f.: exp(-x) - exp(-2*x). a(n) = -2 * a(n-1) - (-1)^n if n>0. a(n) = -(-1)^n * A000225(n). a(n) = -3 * a(n-1) - 2 * a(n-2) if n>1. REVERT transform is A001003 omitting a(0)=0. INVERT transform is A108520. 2^n = a(n+1)^2 - a(n) * a(n+2). |a(n)| = A168604(n+2)= A000225(n). EXAMPLE G.f. = x - 3*x^2 + 7*x^3 - 15*x^4 + 31*x^5 - 63*x^6 + 127*x^7 - 255*x^8 + 511*x^9 + ... MATHEMATICA a[ n_] := If[ n<0, 0, (-1)^n (1 - 2^n)]; LinearRecurrence[{-3, -2}, {0, 1}, 50] (* G. C. Greubel, Aug 09 2018 *) PROG (PARI) {a(n) = if( n<0, 0, (-1)^n * (1 - 2^n))}; (PARI) {a(n) = if( n<0, 0, polcoeff( x / ((1 + x) * (1 + 2*x)) + x * O(x^n), n))}; (MAGMA) [(-1)^n*(1 - 2^n): n in [0..50]]; // G. C. Greubel, Aug 09 2018 CROSSREFS Cf. A000225, A001003, A001047, A108520. Sequence in context: A060152 A126646 A000225 * A255047 A168604 A123121 Adjacent sequences:  A225880 A225881 A225882 * A225884 A225885 A225886 KEYWORD sign,easy AUTHOR Michael Somos, May 19 2013 STATUS approved

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Last modified September 20 01:58 EDT 2019. Contains 327207 sequences. (Running on oeis4.)