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 A245489 a(n) = (1^n + (-2)^n + 4^n)/3. 2
 1, 1, 7, 19, 91, 331, 1387, 5419, 21931, 87211, 349867, 1397419, 5593771, 22366891, 89483947, 357903019, 1431677611, 5726579371, 22906579627, 91625794219, 366504225451, 1466014804651, 5864063412907, 23456245263019, 93824997829291, 375299957762731 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,6,-8). FORMULA G.f.: (1 - 2*x - 2*x^2) / ((1 - x) * (1 + 2*x) * (1 - 4*x)). 0 = 8*a(n) - 6*a(n+1) - 3*a(n+2) + a(n+3) for all n in Z. a(2*n) = A018240(4*n + 3). a(2*n + 1) = A129362(4*n). a(n) = A001045(3*n)/(3*A001045(n)) for n >= 1. - Peter Bala, Apr 06 2015 E.g.f.: (exp(x) + exp(4*x) + exp(-2*x))/3. - G. C. Greubel, Sep 21 2019 EXAMPLE G.f. = 1 + x + 7*x^2 + 19*x^3 + 91*x^4 + 331*x^5 + 1387*x^6 + 5419*x^7 + ... MAPLE seq((1 +(-2)^n +4^n)/3, n=0..30); # G. C. Greubel, Sep 21 2019 MATHEMATICA CoefficientList[Series[(1-2x-2x^2)/((1-x)(1+2x)(1-4x)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 25 2014 *) LinearRecurrence[{3, 6, -8}, {1, 1, 7}, 30] (* Harvey P. Dale, Dec 04 2018 *) PROG (PARI) {a(n) = (1^n + (-2)^n + 4^n) / 3}; (PARI) {a(n) = if( n<0, 4^n, 1) * polcoeff( (1 - 2*x - 2*x^2) / ((1 - x) * (1 + 2*x) * (1 - 4*x)) + x * O(x^abs(n)), abs(n))}; (Magma) [(1^n + (-2)^n + 4^n) / 3 : n in [0..30]]; // Vincenzo Librandi, Jul 25 2014 (Sage) [(1 +(-2)^n +4^n)/3 for n in (0..30)] # G. C. Greubel, Sep 21 2019 (GAP) List([0..30], n-> (1 +(-2)^n +4^n)/3); # G. C. Greubel, Sep 21 2019 CROSSREFS Cf. A001045, A018240, A129362. Sequence in context: A088988 A109879 A109880 * A084603 A088883 A262186 Adjacent sequences: A245486 A245487 A245488 * A245490 A245491 A245492 KEYWORD nonn,easy AUTHOR Michael Somos, Jul 23 2014 STATUS approved

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Last modified December 5 04:50 EST 2022. Contains 358578 sequences. (Running on oeis4.)