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 A195241 Expansion of (1-x+19*x^3-3*x^4)/(1-x)^3. 3
 1, 2, 3, 23, 59, 111, 179, 263, 363, 479, 611, 759, 923, 1103, 1299, 1511, 1739, 1983, 2243, 2519, 2811, 3119, 3443, 3783, 4139, 4511, 4899, 5303, 5723, 6159, 6611, 7079, 7563, 8063, 8579, 9111, 9659, 10223, 10803, 11399, 12011, 12639, 13283, 13943 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sequence found by reading the line 1, 2, 3, 23,.. in the square spiral whose vertices are the triangular numbers (A000217) - see Pol's comments in other sequences visible in this numerical spiral. This is a subsequence of A110326 (without signs) and  A047838 (apart from the second term, 2). LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 Bruno Berselli, Illustration of initial terms: An origin of A195241. Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1). FORMULA G.f.: (1-x+19*x^3-3*x^4)/(1-x)^3. a(n) = 8*n^2-20*n+11 for n>1; a(0)=1, a(1)=2. MATHEMATICA CoefficientList[Series[(1 - x + 19 x^3 - 3 x^4)/(1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Mar 26 2013 *) PROG (PARI) Vec((1-x+19*x^3-3*x^4)/(1-x)^3+O(x^44)) (MAGMA) m:=44; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x+19*x^3-3*x^4)/(1-x)^3)); (Maxima) makelist(coeff(taylor((1-x+19*x^3-3*x^4)/(1-x)^3, x, 0, n), x, n), n, 0, 43); CROSSREFS Cf. A000217. Cf. A033585, A069129, A077221, A102083, A139098, A139271-A139277, A139592, A139593, A188135, A194268, A194431, A195605 [incomplete list]. Sequence in context: A199342 A120366 A041787 * A090180 A009130 A093504 Adjacent sequences:  A195238 A195239 A195240 * A195242 A195243 A195244 KEYWORD nonn,easy AUTHOR Bruno Berselli, Sep 13 2011 - based on remarks and sequences by Omar E. Pol. STATUS approved

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