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 A105770 Expansion of (x^2-x+1)(4x^2+x+1) / ((1+x+x^2)(1-x)^3). 2
 1, 2, 7, 10, 17, 28, 37, 50, 67, 82, 101, 124, 145, 170, 199, 226, 257, 292, 325, 362, 403, 442, 485, 532, 577, 626, 679, 730, 785, 844, 901, 962, 1027, 1090, 1157, 1228, 1297, 1370, 1447, 1522, 1601, 1684, 1765, 1850, 1939, 2026, 2117, 2212, 2305, 2402, 2503 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This sequence is "tesrokseq" at the link "Sequences in Context". The identity vesrok = jesrok + lesrok + tesrok holds. Differs from A002522 (n^2+1) by two every third number. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1). FORMULA a(n) = n^2 + 1 + [0,0,2] (3-periodic). - Ralf Stephan, Nov 15 2010. a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5) for n>4. - Colin Barker, May 19 2019 MATHEMATICA LinearRecurrence[{2, -1, 1, -2, 1}, {1, 2, 7, 10, 17}, 51] (* Ray Chandler, Sep 23 2015 *) PROG Floretion Algebra Multiplication Program, FAMP Code: 4tesrokseq[ - .25'i + 1.25'j - .25'k - .25i' + 1.25j' - .25k' + 1.25'ii' + .25'jj' - .75'kk' + .75'ij' + .25'ik' + .75'ji' - .25'jk' + .25'ki' - .25'kj' + .25e] (Link to Sequences in Context contains further details on the "roktype" used). (PARI) Vec((1 - x + x^2)*(1 + x + 4*x^2) / ((1 - x)^3*(1 + x + x^2)) + O(x^60)) \\ Colin Barker, May 19 2019 CROSSREFS Cf. A105771, A105772, A002522. Sequence in context: A295825 A140115 A294865 * A240469 A257335 A152211 Adjacent sequences:  A105767 A105768 A105769 * A105771 A105772 A105773 KEYWORD easy,nonn AUTHOR Creighton Dement, Apr 18 2005 STATUS approved

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Last modified January 19 13:08 EST 2021. Contains 340269 sequences. (Running on oeis4.)