This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A028326 Twice Pascal's triangle A007318: T(n,k) = 2*C(n,k). 15
 2, 2, 2, 2, 4, 2, 2, 6, 6, 2, 2, 8, 12, 8, 2, 2, 10, 20, 20, 10, 2, 2, 12, 30, 40, 30, 12, 2, 2, 14, 42, 70, 70, 42, 14, 2, 2, 16, 56, 112, 140, 112, 56, 16, 2, 2, 18, 72, 168, 252, 252, 168, 72, 18, 2, 2, 20, 90, 240, 420, 504, 420, 240, 90, 20, 2, 2, 22, 110, 330, 660, 924 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Also number of binary vectors of length n+1 with k+1 runs (1<=k<=n). If the last two entries in each row are removed and 0 replaces the entries in a checkerboard pattern, we obtain   2;   0,  6;   2,  0, 12;   0, 10,  0,  20;   2,  0, 30,   0,  30;   0, 14,  0,  70,   0,  42;   2,  0, 56,   0, 140,   0, 56;   0, 18,  0, 168,   0, 252,  0, 72;   ... This plays the same role of recurrence coefficients for second differences of polynomials as triangle A074909 plays for the first differences. - R. J. Mathar, Jul 03 2013 REFERENCES I. Goulden and D. Jackson, Combinatorial Enumeration, John Wiley and Sons, 1983, page 76. LINKS Reinhard Zumkeller, Rows n=0..150 of triangle, flattened R. J. Mathar, Paving rectangular regions with rectangular tiles: tatami and non-tatami tilings, arXiv:1311.6135 [math.CO], 2013, Table 48. Franck Ramaharo, Statistics on some classes of knot shadows, arXiv:1802.07701 [math.CO], 2018. FORMULA G.f. for the number of length n binary words with k runs: (1-x+x*y)/(1-x-x*y) [Goulden and Jackson]. - Geoffrey Critzer, Mar 04 2012 EXAMPLE Triangle begins: 2 2,  2 2,  4,   2 2,  6,   6,   2 2,  8,  12,   8,   2 2, 10,  20,  20,  10,    2 2, 12,  30,  40,  30,   12,    2 2, 14,  42,  70,  70,   42,   14,    2 2, 16,  56, 112, 140,  112,   56,   16,   2 2, 18,  72, 168, 252,  252,  168,   72,  18,   2 2, 20,  90, 240, 420,  504,  420,  240,  90,  20,   2 2, 22, 110, 330, 660,  924,  924,  660, 330, 110,  22,  2 2, 24, 132, 440, 990, 1584, 1848, 1584, 990, 440, 132, 24, 2 MAPLE T := proc(n, k) if k=0 then 2 elif k>n then 0 else T(n-1, k)+T(n-1, k-1) fi end: for n from 0 to 13 do seq(T(n, k), k=0..n) od; # Zerinvary Lajos, Dec 16 2006 MATHEMATICA Table[2*Binomial[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Robert G. Wilson v, Mar 05 2012 *) PROG (Haskell) a028326 n k = a028326_tabl !! n !! k a028326_row n = a028326_tabl !! n a028326_tabl = iterate    (\row -> zipWith (+) ([0] ++ row) (row ++ [0])) [2] -- Reinhard Zumkeller, Mar 12 2012 (PARI) T(n, k) = 2*binomial(n, k) \\ Charles R Greathouse IV, Feb 07 2017 (Python) from sympy import binomial def T(n, k): return 2*binomial(n, k) for n in xrange(21): print [T(n, k) for k in xrange(n + 1)] # Indranil Ghosh, Apr 29 2017 CROSSREFS Cf. A028327, A007318. Sequence in context: A237709 A250200 A097859 * A156046 A048003 A098219 Adjacent sequences:  A028323 A028324 A028325 * A028327 A028328 A028329 KEYWORD nonn,tabl,easy,nice AUTHOR EXTENSIONS More terms from Donald Manchester, Jr. (s1199170(AT)cedarnet.cedarville.edu) 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.

Last modified September 16 08:53 EDT 2019. Contains 327092 sequences. (Running on oeis4.)