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%I #26 Mar 07 2024 16:02:21
%S 1,2,7,10,17,28,37,50,67,82,101,124,145,170,199,226,257,292,325,362,
%T 403,442,485,532,577,626,679,730,785,844,901,962,1027,1090,1157,1228,
%U 1297,1370,1447,1522,1601,1684,1765,1850,1939,2026,2117,2212,2305,2402,2503
%N Expansion of (x^2-x+1)*(4*x^2+x+1) / ((1+x+x^2)*(1-x)^3).
%C This sequence is "tesrokseq" at the link "Sequences in Context". The identity vesrok = jesrok + lesrok + tesrok holds.
%C 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).
%C Differs from A002522 (n^2+1) by two every third number.
%H Colin Barker, <a href="/A105770/b105770.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).
%F a(n) = n^2 + 1 + [0,0,2] (3-periodic). - _Ralf Stephan_, Nov 15 2010.
%F 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
%F 3*a(n) = 3*n^2 +5 -2*A061347(n). - _R. J. Mathar_, Oct 25 2022
%t LinearRecurrence[{2, -1, 1, -2, 1},{1, 2, 7, 10, 17},51] (* _Ray Chandler_, Sep 23 2015 *)
%o (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
%Y Cf. A105771, A105772, A002522.
%K easy,nonn
%O 0,2
%A _Creighton Dement_, Apr 18 2005
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