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A109794 a(2n) = A001906(n+1), a(2n+1) = A002878(n). 2
1, 1, 3, 4, 8, 11, 21, 29, 55, 76, 144, 199, 377, 521, 987, 1364, 2584, 3571, 6765, 9349, 17711, 24476, 46368, 64079, 121393, 167761, 317811, 439204, 832040, 1149851, 2178309, 3010349, 5702887, 7881196, 14930352, 20633239, 39088169 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Sequence relates bisections of Lucas and Fibonacci numbers (see also A098149).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index to sequences with linear recurrences with constant coefficients, signature (0,3,0,-1)

FORMULA

G.f.: (1+x+x^3)/((x^2-x-1)*(x^2+x-1)).

a(n) = (3/20*sqrt(5)+3/4)*(1/2+1/2*sqrt(5))^n + (-3/20*sqrt(5)+3/4)*(1/2-1/2 *sqrt(5))^n + (-3/20*sqrt(5)-1/4)*(-1/2+1/2*sqrt(5))^n +(3/20*sqrt(5)-1/4) *(-1/2-1/2*sqrt(5))^n.

a(n) = 3*a(n-2)-a(n-4), n >= 4; a(0) = 1, a(1) = 1, a(2) = 3, a(3) = 4. - Daniel Forgues, May 07 2011

MAPLE

a:= n-> (<<0|1>, <-1|3>>^iquo(n, 2, 'r'). <<1, 3+r>>)[1, 1]:

seq (a(n), n=0..50);  # Alois P. Heinz, May 02 2011

PROG

Floretion Algebra Multiplication Program, FAMP code: 4jesleftforsumseq[ + .25'i + .25i' + .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' + .25e], vesleftforsumseq = A000045, sumtype: (Y[15], *, inty*sum) (internal program code)

CROSSREFS

Cf. A001906, A002878, A098149, A000045, A189761.

Sequence in context: A006167 A137504 A173401 * A034417 A126873 A050316

Adjacent sequences:  A109791 A109792 A109793 * A109795 A109796 A109797

KEYWORD

nonn,easy

AUTHOR

Creighton Dement, Aug 14 2005

STATUS

approved

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Last modified October 31 05:13 EDT 2014. Contains 248845 sequences.