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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A102543 Antidiagonal sums of the antidiagonals of Losanitsch's triangle. 5
1, 1, 1, 2, 2, 3, 4, 6, 8, 12, 16, 24, 33, 49, 69, 102, 145, 214, 307, 452, 653, 960, 1393, 2046, 2978, 4371, 6376, 9354, 13665, 20041, 29307, 42972, 62884, 92191, 134974, 197858, 289772, 424746, 622198, 911970, 1336121, 1958319, 2869417, 4205538, 6162579, 9031996, 13235661, 19398240 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The Ca1 and Ca2 sums, see A180662 for their definitions, of Losanitsch's triangle A034851 equal this sequence. - Johannes W. Meijer, Jul 14 2011

For n >= 5, a(n+1)-1 is the number of non-isomorphic snake polyominoes with n cells that can be inscribed in a rectangle of height 2. - Christian Barrientos and Sarah Minion, Jul 29 2018

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

R. J. Mathar, Paving rectangular regions with rectangular tiles: Tatami and Non-Tatami Tilings, arXiv:1311.6135 [math.CO], 2013, Table 25.

Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-1,1,-1,0,-1).

FORMULA

a(n) = A068927(n-1), n>3.

From Johannes W. Meijer, Jul 14 2011: (Start)

G.f.: (-1/2)*(1/(x^3+x-1)+(1+x+x^3)/(x^6+x^2-1))= ( 1-x^2-x^4-x^6 ) / ( (x^3+x-1)*(x^6+x^2-1) ).

a(n) = (A000930(n)+x(n)+x(n-1)+x(n-3))/2 with x(2*n) = A000930(n) and x(2*n+1) = 0. (End)

MAPLE

A102543 := proc(n): (A000930(n)+x(n)+x(n-1)+x(n-3))/2 end: A000930:=proc(n): sum(binomial(n-2*i, i), i=0..n/3) end: x:=proc(n): if type(n, even) then A000930(n/2) else 0 fi: end: seq(A102543(n), n=0..38); # Johannes W. Meijer, Jul 14 2011

MATHEMATICA

CoefficientList[Series[(1 - x^2 - x^4 - x^6)/((x^3 + x - 1)*(x^6 + x^2 - 1)), {x, 0, 50}], x] (* G. C. Greubel, Apr 27 2017 *)

PROG

(PARI) x='x+O('x^50); Vec((1 - x^2 - x^4 - x^6)/((x^3 + x - 1)*(x^6 + x^2 - 1))) \\ G. C. Greubel, Apr 27 2017

CROSSREFS

Cf. A034851 A068927, A102451.

Sequence in context: A006207 A318403 A017912 * A316076 A068598 A293165

Adjacent sequences:  A102540 A102541 A102542 * A102544 A102545 A102546

KEYWORD

nonn

AUTHOR

Gerald McGarvey, Feb 24 2005

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 17 01:09 EDT 2018. Contains 316275 sequences. (Running on oeis4.)