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 A212336 Expansion of 1/(1-23*x+23*x^2-x^3). 17
 1, 23, 506, 11110, 243915, 5355021, 117566548, 2581109036, 56666832245, 1244089200355, 27313295575566, 599648413462098, 13164951800590591, 289029291199530905, 6345479454589089320, 139311518709760434136, 3058507932160140461673 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Partial sums of A077421. LINKS Bruno Berselli, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (23,-23,1). FORMULA G.f.: 1/((1-x)*(1-22*x+x^2)). a(n) = (((6+sqrt(30))^(2n+3)+(6-sqrt(30))^(2n+3))/6^(n+1)-12)/240. a(n) = a(-n-3) = 23*a(n-1)-23*a(n-2)+a(n-3). a(n)*a(n+2) = a(n+1)*(a(n+1)-1). a(n+1)-11*a(n) = A133285(n+2). 11*a(n+1)-a(n) = (1/5)*A157096(n+2). MAPLE a:= n-> (<<0|1|0>, <0|0|1>, <1|-23|23>>^n. <<1, 23, 506>>)[1, 1]: seq(a(n), n=0..20);  # Alois P. Heinz, Jun 15 2012 MATHEMATICA CoefficientList[Series[1/(1 - 23 x + 23 x^2 - x^3), {x, 0, 16}], x] LinearRecurrence[{23, -23, 1}, {1, 23, 506}, 20] (* Vincenzo Librandi, Aug 18 2013 *) PROG (PARI) Vec(1/(1-23*x+23*x^2-x^3)+O(x^17)) (Maxima) makelist(coeff(taylor(1/(1-23*x+23*x^2-x^3), x, 0, n), x, n), n, 0, 16); (MAGMA) m:=17; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-23*x+23*x^2-x^3))); (MAGMA) I:=[1, 23, 506]; [n le 3 select I[n] else 23*Self(n-1)-23*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Aug 18 2013 CROSSREFS Sequences with g.f. of the type 1/(1-k*x+k*x^2-x^3): A212335 (k=22), A097833 (k=21), A097832 (k=20), A049664 (k=19), A097831-A097829 (k=18,17,16), A076139 (k=15), A097828-A097826 (k=14,13,12), A097784 (k=11), A092420 (k=10), A076765 (k=9), A092521 (k=8), A053142 (k=7), A089817(k=6), A061278 (k=5), A027941 (k=4), A000217 (k=3), A021823 (k=2), A133872 (k=1), A079978 (k=0). Sequence in context: A133283 A121903 A162809 * A163171 A163518 A163991 Adjacent sequences:  A212333 A212334 A212335 * A212337 A212338 A212339 KEYWORD nonn,easy AUTHOR Bruno Berselli, Jun 08 2012 STATUS approved

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Last modified October 15 04:33 EDT 2019. Contains 328026 sequences. (Running on oeis4.)