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A111352 a(n+3) = a(n+2) + 3*a(n+1) + a(n). 0
1, -1, 2, 0, 5, 7, 22, 48, 121, 287, 698, 1680, 4061, 9799, 23662, 57120, 137905, 332927, 803762, 1940448, 4684661, 11309767, 27304198, 65918160, 159140521, 384199199, 927538922, 2239277040, 5406093005 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) + a(n+1) = A000129(n); a(n+2) - a(n) = A001333(n)

REFERENCES

C. Dement, Floretion-generated Integer Sequences (work in progress)

LINKS

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (1,3,1).

FORMULA

a(n) = (1/4*sqrt(2)-1/4)*(1+sqrt(2))^n + (-1/4*sqrt(2)-1/4)*(1-sqrt(2))^n + 3/2*(-1)^n; G.f. (2*x-1)/((x+1)*(x^2+2*x-1))

a(n) = 3*(-1)^n/2+A001333(n-1)/2, n>0. [From R. J. Mathar, Nov 10 2009]

PROG

Floretion Algebra Multiplication Program, FAMP Code: 2jbasekrokseq[A*H] with A = + .25'i + .25i' + .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' + .25e; H = - 2'i - 'j + 'k; roktype : Y[15] = Y[15] + (-1)^p (internal program code)

CROSSREFS

Cf. A000129, A001333.

Sequence in context: A021490 A084258 A171016 * A173343 A133446 A011122

Adjacent sequences:  A111349 A111350 A111351 * A111353 A111354 A111355

KEYWORD

easy,sign

AUTHOR

Creighton Dement, Oct 29 2005

STATUS

approved

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Last modified March 28 22:27 EDT 2017. Contains 284249 sequences.