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 A201780 Riordan array ((1-x)^2/(1-2x), x/(1-2x)). 10
 1, 0, 1, 1, 2, 1, 2, 5, 4, 1, 4, 12, 13, 6, 1, 8, 28, 38, 25, 8, 1, 16, 64, 104, 88, 41, 10, 1, 32, 144, 272, 280, 170, 61, 12, 1, 64, 320, 688, 832, 620, 292, 85, 14, 1, 128, 704, 1696, 2352, 2072, 1204, 462, 113, 16, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Diagonals ascending: 1, 0, 1, 1, 2, 2, 4, 5, 1, 8, 12, 4, ... (see A201509). LINKS Benjamin Braun, W. K. Hough, Matching and Independence Complexes Related to Small Grids, arXiv preprint arXiv:1606.01204 [math.CO], 2016. Wesley K. Hough, On Independence, Matching, and Homomorphism Complexes, (2017), Theses and Dissertations--Mathematics, 42. FORMULA T(n,k) = 2*T(n-1,k) + T(n-1,k-1) with T(0,0) = 0, T(1,0) = 0, T(2,0) = 0 and T(n,k)= 0 if k < 0 or if n < k. Sum_{k=0..n} T(n,k)*x^k = A154955(n+1), A034008(n), A052156(n), A055841(n), A055842(n), A055846(n), A055270(n), A055847(n), A055995(n), A055996(n), A056002(n), A056116(n) for x = -1,0,1,2,3,4,5,6,7,8,9,10 respectively. G.f.: (1-x)^2/(1-(y+2)*x). EXAMPLE Triangle begins:   1;   0,  1;   1,  2,  1;   2,  5,  4,  1;   4, 12, 13,  6,  1;   8, 28, 38, 25,  8,  1; MATHEMATICA CoefficientList[#, y]& /@ CoefficientList[(1-x)^2/(1-(y+2)*x) + O[x]^10, x] // Flatten (* Jean-François Alcover, Nov 03 2018 *) CROSSREFS Diagonals: A000012, A005843, A001844, A035597, Columns: A034008, A045623, A084851, A055585, Row sums: A052156 Sequence in context: A099602 A151703 A151691 * A104560 A121435 A137156 Adjacent sequences:  A201777 A201778 A201779 * A201781 A201782 A201783 KEYWORD nonn,tabl AUTHOR Philippe Deléham, Dec 05 2011 STATUS approved

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Last modified February 18 02:15 EST 2019. Contains 320237 sequences. (Running on oeis4.)