

A100828


Expansion of (1+2*x2*x^33*x^2)/((x1)*(x+1)*(x^2+2*x1)).


11



1, 4, 7, 18, 41, 100, 239, 578, 1393, 3364, 8119, 19602, 47321, 114244, 275807, 665858, 1607521, 3880900, 9369319, 22619538, 54608393, 131836324, 318281039, 768398402, 1855077841, 4478554084, 10812186007, 26102926098, 63018038201
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OFFSET

0,2


COMMENTS

A floretiongenerated sequence relating NSW and Pell numbers.
Elements of odd index in the sequence gives A002315. a(n+2)  a(n) = A002203(n+2).


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
Robert Munafo, Sequences Related to Floretions
Index entries for linear recurrences with constant coefficients, signature (2,2,2,1).


FORMULA

a(n) = (u^(n+1)+1)*(v^(n+1)+1)/2 with u = 1+sqrt(2), v = 1sqrt(2).  Vladeta Jovovic, May 30 2007
From Colin Barker, Apr 29 2019: (Start)
G.f.: (1 + 2*x  3*x^2  2*x^3) / ((1  x)*(1 + x)*(1  2*x  x^2)).
a(n) = (1 + (1)^(1+n) + (1sqrt(2))^(1+n) + (1+sqrt(2))^(1+n)) / 2.
a(n) = 2*a(n1) + 2*a(n2)  2*a(n3)  a(n4) for n>3.
(End)


PROG

Floretion Algebra Multiplication Program, FAMP
Floretion Algebra Multiplication Program, FAMP Code: 2tesseq[B*C} with B =  .25'i + .25'j + .5'k  .25i' + .25j' + .5k'  .5'kk'  .25'ik'  .25'jk'  .25'ki'  .25'kj'  .5e and C = + .5'i  .25'j + .25'k + .5i'  .25j' + .25k'  .5'ii'  .25'ij'  .25'ik'  .25'ji'  .25'ki'  .5e
(PARI) Vec((1 + 2*x  3*x^2  2*x^3) / ((1  x)*(1 + x)*(1  2*x  x^2)) + O(x^30)) \\ Colin Barker, Apr 29 2019


CROSSREFS

Cf. A002315, A002203.
Sequence in context: A077920 A234269 A135582 * A267488 A230601 A132207
Adjacent sequences: A100825 A100826 A100827 * A100829 A100830 A100831


KEYWORD

easy,nonn


AUTHOR

Creighton Dement, Jan 06 2005; revised Aug 22 2005


STATUS

approved



