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 A144112 Weight array W={w(i,j)} of the natural number array A000027. 63
 1, 1, 2, 2, 1, 3, 3, 1, 1, 4, 4, 1, 1, 1, 5, 5, 1, 1, 1, 1, 6, 6, 1, 1, 1, 1, 1, 7, 7, 1, 1, 1, 1, 1, 1, 8, 8, 1, 1, 1, 1, 1, 1, 1, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 10, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The lattice lines in the first quadrant (including the x and y axes) cut the plane into unit squares.  Suppose a weight w(i,j) is assigned to the square that has as upper right corner the point (i,j).  Let s(m,n) be the sum of the weights w(i,j) for 1<=i<=m, 1<=j<=n.  We call the array W={w(i,j)} the weight array of the array S={s(m,n)} and S the accumulation array of W.  For the case at hand, S is the array of natural numbers having the following antidiagonals: (1), then (2,3), then (4,5,6), then (7,8,9,10) and so on. Contribution from Clark Kimberling, Sep 14 2008: (Start) In general, the weight array W of an arbitrary rectangular array S={s(i,j): i>=1, j>=1} is defined in two steps: (1) extend s by defining s(i,j)=0 if i=0 or j=0; (2) then w(m,n)=s(m,n)+s(m-1,n-1)-s(m,n-1)-s(m-1,n) for m>=1, n>=1. (End) LINKS FORMULA row 1: 1 followed by A000027 row n: n followed by A000012, for n>1. EXAMPLE Northwest corner: 1 1 2 3 4 5 2 1 1 1 1 1 3 1 1 1 1 1 4 1 1 1 1 1 5 1 1 1 1 1. so that the accumulation array has corner 1...2...4...7...11...16 3...5...8...12..17...23 6...9...13..18..24...31 10..14..19..25..32...40 15..20..26..33..41...50. s(2,4)=1+1+2+3+2+1+1+1=12. CROSSREFS Cf. A000012, A000027. Sequence in context: A103360 A267409 A104469 * A178568 A104660 A212125 Adjacent sequences:  A144109 A144110 A144111 * A144113 A144114 A144115 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Sep 11 2008 EXTENSIONS Example by Clark Kimberling, Jan 31 2011 STATUS approved

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Last modified August 13 05:41 EDT 2020. Contains 336442 sequences. (Running on oeis4.)