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 A267541 Expansion of (2 + 4*x + x^2 + x^3 + 2*x^4 + x^5)/(1 - x - x^5 + x^6). 4
 2, 6, 7, 8, 10, 13, 17, 18, 19, 21, 24, 28, 29, 30, 32, 35, 39, 40, 41, 43, 46, 50, 51, 52, 54, 57, 61, 62, 63, 65, 68, 72, 73, 74, 76, 79, 83, 84, 85, 87, 90, 94, 95, 96, 98, 101, 105, 106, 107, 109, 112, 116, 117, 118, 120, 123, 127, 128, 129, 131, 134, 138, 139, 140 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Also, numbers that are congruent to {2, 6, 7, 8, 10} mod 11. (m^k+1)/11 is a nonnegative integer when . m is a member of this sequence and k is an odd multiple of 5 (A017329), . m is a member of A017509 and k is odd but not multiple of 5 (A045572). If k is even, (m^k+1)/11 is never an integer. The product of two terms does not belong to the sequence. LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1). FORMULA G.f.: (2 + 4*x + x^2 + x^3 + 2*x^4 + x^5)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)). a(n) = a(n-1) + a(n-5) - a(n-6). a(-n) = -A267755(n-1). EXAMPLE From the linear recurrence: (-A267755) ..., -12, -9, -5, -4, -3, -1, 2, 6, 7, 8, 10, 13, ... (A267541) MAPLE gf := (2+4*x+x^2+x^3+2*x^4+x^5)/((1-x)^2*(1+x+x^2+x^3+ x^4)): deg := 64: series(gf, x, deg): seq(coeff(%, x, n), n=0..deg-1); # Peter Luschny, Jan 19 2016 MATHEMATICA CoefficientList[Series[(2 + 4 x + x^2 + x^3 + 2 x^4 + x^5)/(1 - x - x^5 + x^6), {x, 0, 70}], x] LinearRecurrence[{1, 0, 0, 0, 1, -1}, {2, 6, 7, 8, 10, 13}, 70] Select[Range[150], MemberQ[{2, 6, 7, 8, 10}, Mod[#, 11]]&] PROG (PARI) Vec((2+4*x+x^2+x^3+2*x^4+x^5)/(1-x-x^5+x^6)+O(x^70)) (Magma) m:=70; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((2+4*x+x^2+x^3+2*x^4+x^5)/(1-x-x^5+x^6))); (Sage) gf = (2+4*x+x^2+x^3+2*x^4+x^5)/((1-x)^2*(1+x+x^2+x^3+ x^4)) print(taylor(gf, x, 0, 63).list()) # Peter Luschny, Jan 19 2016 CROSSREFS Cf. A002266, A017329, A017509, A267755. Cf. A088225: numbers congruent to {2,6,7,8} mod 11. Sequence in context: A355160 A343719 A028735 * A325465 A047553 A139418 Adjacent sequences: A267538 A267539 A267540 * A267542 A267543 A267544 KEYWORD nonn,easy AUTHOR Bruno Berselli, Jan 16 2016 STATUS approved

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Last modified June 19 16:32 EDT 2024. Contains 373503 sequences. (Running on oeis4.)