login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A110679 a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 1, a(1) = 2, a(2) = 11. 7
1, 2, 11, 44, 189, 798, 3383, 14328, 60697, 257114, 1089155, 4613732, 19544085, 82790070, 350704367, 1485607536, 6293134513, 26658145586, 112925716859, 478361013020, 2026369768941, 8583840088782, 36361730124071, 154030760585064, 652484772464329 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

2tesseq[A*B*cyc(A)] (see program code) gives an alternative formula for A110528.

a(n) is the number of tilings of a 2 X n rectangle by using 1 X 1 squares, dominoes and right trominoes. - Roberto Tauraso, Mar 21 2017

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Robert Munafo, Sequences Related to Floretions

Hermann Stamm-Wilbrandt, 6 interlaced bisections

Index entries for linear recurrences with constant coefficients, signature (3,5,1).

FORMULA

Program "FAMP" finds: 2*(-1^(n+1)) = A110528(n) - A001076(n+1) - 2*a(n). Program "Superseeker" finds: a(n) = A110526(n+1) - A110526(n); a(n) + a(n+1) = A033887(n+1).

a(n) = (-1)^n*Sum_{k=0..n} (-1)^k*Fibonacci(3*k+1). - Gary Detlefs, Jan 22 2013

a(n) = (Fibonacci(3*n+2)+(-1)^n)/2. - Roberto Tauraso, Mar 21 2017

From Colin Barker, Mar 21 2017: (Start)

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

a(n) = 3*a(n-1) + 5*a(n-2) + a(n-3) for n>2.

(End)

a(n) = -(-1)^n * A049651(-1 - n) for all n in Z. - Michael Somos, Mar 26 2017

a(2*n) = A254627(2*n+1); a(2*n+1) = A077259(2*n+1). See "6 interlaced bisections" link. - Hermann Stamm-Wilbrandt, Apr 18 2019

EXAMPLE

G.f. = 1 + 2*x + 11*x^2 + 44*x^3 + 189*x^4 + 798*x^5 + 3383*x^6 + 14328*x^7 + ...

MAPLE

seriestolist(series((-1+x)/((x+1)*(x^2+4*x-1)), x=0, 25)); -or- Floretion Algebra Multiplication Program, FAMP Code: -1jesseq[A*B*cyc(A)] with A = - 'j + 'k - 'ii' - 'ij' - 'ik' and B = - .5'i - .5i' - .5'ii' + .5'jj' - .5'kk' + .5'jk' + .5'kj' - .5e

MATHEMATICA

a[n_] := (Fibonacci[3*n+2] + (-1)^n)/2; a /@ Range[0, 22] (* Giovanni Resta, Mar 21 2017 *)

PROG

(PARI) Vec((1 - x) / ((1 + x)*(1 - 4*x - x^2)) + O(x^30)) \\ Colin Barker, Mar 21 2017

(PARI) {a(n) = -(-1)^n * (fibonacci(-2 - 3*n)\2)}; /* Michael Somos, Mar 26 2017 */

(MAGMA) [(Fibonacci(3*n+2) +(-1)^n)/2: n in [0..30]]; // G. C. Greubel, Apr 19 2019

(Sage) [(fibonacci(3*n+2) +(-1)^n)/2 for n in (0..30)] # G. C. Greubel, Apr 19 2019

CROSSREFS

Cf. A110528, A110680, A001076, A110526, A110526, A033887.

Sequence in context: A037744 A037625 A181270 * A127109 A054208 A257066

Adjacent sequences:  A110676 A110677 A110678 * A110680 A110681 A110682

KEYWORD

easy,nonn

AUTHOR

Creighton Dement, Aug 02 2005

EXTENSIONS

Typo in program code fixed by Creighton Dement, Dec 11 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 08:49 EST 2019. Contains 329862 sequences. (Running on oeis4.)