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A110526 a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 0, a(1) = 1, a(2) = 3. 4
0, 1, 3, 14, 58, 247, 1045, 4428, 18756, 79453, 336567, 1425722, 6039454, 25583539, 108373609, 459077976, 1944685512, 8237820025, 34895965611, 147821682470, 626182695490, 2652552464431, 11236392553213, 47598122677284 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A001076(n) = a(n) + a(n+1). Program "Superseeker" finds: A033887(n+1) = a(n+2) - a(n); Elements of even index in the sequence: A049661(n) = (F(6n+1)-1)/4; A015448(n+2) = a(n+2) + 2*a(n+1) + a(n)

LINKS

Table of n, a(n) for n=0..23.

FORMULA

G.f.: -x/((1+x)*(x^2+4*x-1).

a(n) = (1/8)*[2-sqrt(5)]^n-(1/4)*(-1)^n+(1/8)*[2+sqrt(5)]^n+(1/40)*[2+sqrt(5)]^n*sqrt(5)-(1/40) *[2-sqrt(5)]^n*sqrt(5), with n>=0. [Paolo P. Lava, Oct 02 2008]

a(n) = (-1)^n/2 * sum(k=0..n, (-1)^k*Fibonacci(3*k)). [Gary Detlefs, Jan 03 2013]

a(n) = (Fibonacci(3*n+1)-(-1)^n)/4, where Fibonacci(n) = A000045(n). - Vladimir Reshetnikov, Oct 28 2015

MAPLE

seriestolist(series(-x/((1+x)*(x^2+4*x-1)), x=0, 25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 1jbaseseq[(- 'i + 'j - i' + j' - 'kk' - 'ik' - 'jk' - 'ki' - 'kj')(+ .5'i + .5i' + .5'jj' + .5'kk')]

MATHEMATICA

Table[(Fibonacci[3n+1]-(-1)^n)/4, {n, 0, 20}] (* Vladimir Reshetnikov, Oct 28 2015 *)

PROG

(PARI) concat(0, Vec(x/((1+x)*(1-x^2-4*x)) + O(x^100))) \\ Altug Alkan, Oct 28 2015

CROSSREFS

Cf. A110526, A110527, A033887, A001076, A049661, A033887, A000045.

Sequence in context: A127363 A133444 A126875 * A038679 A151235 A151236

Adjacent sequences:  A110523 A110524 A110525 * A110527 A110528 A110529

KEYWORD

easy,nonn

AUTHOR

Creighton Dement, Jul 24 2005

STATUS

approved

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Last modified December 5 07:11 EST 2016. Contains 278761 sequences.