

A105770


Expansion of (x^2x+1)(4x^2+x+1) / ((1+x+x^2)(1x)^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
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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] (3periodic).  Ralf Stephan, Nov 15 2010.
a(n) = 2*a(n1)  a(n2) + a(n3)  2*a(n4) + a(n5) 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



