The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A226048 Irregular triangle read by rows: T(n,k) is the number of binary pattern classes in the (2,n)-rectangular grid with k '1's and (2n-k) '0's: two patterns are in same class if one of them can be obtained by a reflection or 180-degree rotation of the other. 41
 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 6, 6, 6, 2, 1, 1, 2, 10, 14, 22, 14, 10, 2, 1, 1, 3, 15, 32, 60, 66, 60, 32, 15, 3, 1, 1, 3, 21, 55, 135, 198, 246, 198, 135, 55, 21, 3, 1, 1, 4, 28, 94, 266, 508, 777, 868, 777, 508, 266, 94, 28, 4, 1, 1, 4, 36 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Sum of rows (see example) gives A225826. This triangle is to A225826 as Losanitsch's triangle A034851 is to A005418. By columns: T(n,1) is A004526. T(n,2) is A000217. T(n,3) is A225972. T(n,4) is A071239. T(n,5) is A222715. T(n,6) is A228581. T(n,7) is A228582. T(n,8) is A228583. Also the number of equivalence classes of ways of placing k 1 X 1 tiles in an n X 2 rectangle under all symmetry operations of the rectangle. - Christopher Hunt Gribble, Feb 16 2014 LINKS Yosu Yurramendi and María Merino, Rows 0..40 of triangle, flattened FORMULA If k even, 4*T(n,k) = binomial(2*n,k) +3*binomial(n,k/2). - Yosu Yurramendi, María Merino, Aug 25 2013 If k odd, 4*T(n,k) = 4*T(n,k) = binomial(2*n,k) +(1-(-1)^n)*binomial(n-1,(k-1)/2). - Yosu Yurramendi, María Merino, Aug 25 2013 [corrected by Christian Barrientos, Jun 14 2018] EXAMPLE n\k 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 1 1 1 1 1 2 1 1 3 1 1 3 1 2 6 6 6 2 1 4 1 2 10 14 22 14 10 2 1 5 1 3 15 32 60 66 60 32 15 3 1 6 1 3 21 55 135 198 246 198 135 55 21 3 1 7 1 4 28 94 266 508 777 868 777 508 266 94 28 4 1 8 1 4 36 140... ... The length of row n is 2*n+1, so n>= floor((k+1)/2). MAPLE A226048 := proc(n, k) if type(k, 'even') then binomial(2*n, k) +3*binomial(n, k/2) ; else binomial(2*n, k) +(1-(-1)^n)*binomial(n-1, (k-1)/2) ; end if ; %/4 ; end proc: seq(seq(A226048(n, k), k=0..2*n), n=0..8) ; # R. J. Mathar, Jun 07 2020 MATHEMATICA T[n_, k_] := If[EvenQ[k], Binomial[2n, k] + 3 Binomial[n, k/2], Binomial[2n, k] + (1-(-1)^n) Binomial[n-1, (k-1)/2]]/4; Table[T[n, k], {n, 0, 8}, { k, 0, 2n}] // Flatten (* Jean-François Alcover, May 05 2023 *) CROSSREFS Cf. A225826, A005418, A034851. Sequence in context: A026568 A138361 A030408 * A329210 A325669 A332488 Adjacent sequences: A226045 A226046 A226047 * A226049 A226050 A226051 KEYWORD nonn,tabf AUTHOR Yosu Yurramendi, May 24 2013 EXTENSIONS Definition corrected by María Merino, May 19 2017 STATUS approved

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

Last modified September 29 22:10 EDT 2023. Contains 365781 sequences. (Running on oeis4.)