OFFSET
0,2
COMMENTS
This sequence is "tesrokseq" at the link "Sequences in Context". The identity vesrok = jesrok + lesrok + tesrok holds.
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).
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
3*a(n) = 3*n^2 +5 -2*A061347(n). - R. J. Mathar, Oct 25 2022
MATHEMATICA
LinearRecurrence[{2, -1, 1, -2, 1}, {1, 2, 7, 10, 17}, 51] (* Ray Chandler, Sep 23 2015 *)
PROG
(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
KEYWORD
easy,nonn
AUTHOR
Creighton Dement, Apr 18 2005
STATUS
approved