This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A132885 Triangle read by rows: T(n,k) is the number of paths in the right-half plane from (0,0) to (n,0), consisting of steps U=(1,1), D=(1,-1), h=(1,0) and H=(2,0), having k H=(2,0) steps (0<=k<=floor(n/2)). 4
 1, 1, 3, 1, 7, 2, 19, 9, 1, 51, 28, 3, 141, 95, 18, 1, 393, 306, 70, 4, 1107, 987, 285, 30, 1, 3139, 3144, 1071, 140, 5, 8953, 9963, 3948, 665, 45, 1, 25653, 31390, 14148, 2856, 245, 6, 73789, 98483, 49815, 11844, 1330, 63, 1, 212941, 307836, 172645, 47160 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row n has 1+floor(n/2) terms. T(n,0)=A002426(n) (the central trinomial coefficients). T(n,1)=A109188(n-1). Row sums yield A059345. See A132280 for the same statistic on paths restricted to the first quadrant. LINKS G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened FORMULA G.f.: 1/sqrt((1+z-tz^2)((1-3z-tz^2)). T(n,k) = C(n-k,k)*hypergeom([k-n/2,k-n/2+1/2], [1], 4). - Peter Luschny, Sep 18 2014 EXAMPLE T(4,1)=9 because we have hhH, hHh, Hhh, HUD, UDH, UHD, HDU, DUH and DHU. Triangle starts:                      1;                      1;                  3,      1;                  7,      2;             19,      9,      1;             51,     28,      3;        141,     95,     18,      1;        393,    306,     70,      4;   1107,    987,    285,     30,      1;   3139,   3144,   1071,    140,      5; MAPLE G:=1/sqrt((1+z-t*z^2)*(1-3*z-t*z^2)): Gser:=simplify(series(G, z=0, 18)): for n from 0 to 13 do P[n]:=sort(coeff(Gser, z, n)) end do: for n from 0 to 13 do seq(coeff(P[n], t, j), j=0..floor((1/2)*n)) end do; # yields sequence in triangular form A132885 := (n, k) -> binomial(n-k, k)*hypergeom([k-n/2, k-n/2+1/2], [1], 4): seq(print(seq(round(evalf(A132885(n, k))), k=0..iquo(n, 2))), n=0..9); # Peter Luschny, Sep 18 2014 MATHEMATICA T[n_, k_] := Binomial[n - k, k]*Hypergeometric2F1[k - n/2, k - n/2 + 1/2, 1, 4]; Table[T[n, k], {n, 0, 10}, {k, 0, Floor[n/2]}] // Flatten  (* G. C. Greubel, Mar 01 2017 *) CROSSREFS Cf. A002426, A109188, A059345, A132280. Sequence in context: A235263 A297171 A297156 * A187818 A059090 A133115 Adjacent sequences:  A132882 A132883 A132884 * A132886 A132887 A132888 KEYWORD nonn,tabf AUTHOR Emeric Deutsch, Sep 03 2007 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.

Last modified October 20 18:08 EDT 2018. Contains 316401 sequences. (Running on oeis4.)