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 A152198 Triangle read by rows, A007318 rows repeated 18
 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 20, 15, 6, 1, 1, 6, 15, 20, 15, 6, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Eigensequence of the triangle = A051163: (1, 2, 5, 12, 30, 76,...) Another version of A152815. - Philippe Deléham, Dec 13 2008 Row sums : A016116(n); Diagonal sums: A000931(n+5). - Philippe Deléham, Dec 13 2008 Triangle, with zeros omitted, given by (1, 0, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Jan 16 2012 Sums along rising diagonals are A134816. - John Molokach, Jul 09 2013 LINKS FORMULA Triangle read by rows, Pascal's triangle rows repeated. Equals inverse binomial transform of A133156 unsigned. G.f. : (1+x)/(1-(1+y)*x^2). - Philippe Deléham, Jan 16 2012 Sum_{k, 0<=k<=n} T(n,k)*x^k = A057077(n), A019590(n+1), A000012(n), A016116(n), A108411(n), A074872(n+1) for x = -2, -1, 0, 1, 2, 4 respectively. - Philippe Deléham, Jan 16 2012 T(n,k) = A065941(n-k, n-2*k) = abs(A108299(n-k, n-2*k)). - Johannes W. Meijer, Sep 05 2013 EXAMPLE The triangle starts 1; 1; 1, 1; 1, 1; 1, 2, 1; 1, 2, 1; 1, 3, 3, 1; 1, 3, 3, 1; 1, 4, 6, 4, 1; 1, 4, 6, 4, 1; 1, 5, 10, 10, 5, 1; 1, 5, 10, 10, 5, 1; ... Triangle (1,0,-1,0,0,...) DELTA (0,1,-1,0,0,...) begins: 1 1, 0 1, 1, 0 1, 1, 0, 0 1, 2, 1, 0, 0 1, 2, 1, 0, 0, 0 1, 3, 3, 1, 0, 0, 0 1, 3, 3, 1, 0, 0, 0, 0 1, 4, 6, 4, 1, 0, 0, 0, 0 1, 4, 6, 4, 1, 0, 0, 0, 0, 0 1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0... MATHEMATICA t[n_, k_] := Binomial[ Floor[n/2], k]; Table[t[n, k], {n, 0, 17}, {k, 0, Floor[n/2]}] // Flatten (* Jean-François Alcover, Sep 13 2012 *) CROSSREFS Cf. A007318, A133156, A051163. Sequence in context: A161107 A161042 A029292 * A259342 A258280 A159255 Adjacent sequences:  A152195 A152196 A152197 * A152199 A152200 A152201 KEYWORD nonn,tabf AUTHOR Gary W. Adamson, Nov 28 2008 EXTENSIONS More terms from Philippe Deléham, Dec 14 2008 STATUS approved

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Last modified May 19 22:56 EDT 2019. Contains 323411 sequences. (Running on oeis4.)