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 A152920 Triangle read by rows: triangle A062111 reversed. 11
 0, 1, 1, 2, 3, 4, 3, 5, 8, 12, 4, 7, 12, 20, 32, 5, 9, 16, 28, 48, 80, 6, 11, 20, 36, 64, 112, 192, 7, 13, 24, 44, 80, 144, 256, 448, 8, 15, 28, 52, 96, 176, 320, 576, 1024, 9, 17, 32, 60, 112, 208, 384, 704, 1280, 2304, 10, 19, 36, 68, 128, 240, 448, 832, 1536, 2816 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS FORMULA Row sums: (2^n-1)(n+1)=A058877(n). [R. J. Mathar, Jan 22 2009] T(2n,n) = 3*n*2^(n-1) = 3*A001787(n). [Philippe Deléham, Apr 20 2009] From Werner Schulte, Jul 31 2020: (Start) T(n,k) = (2*n-k) * 2^(k-1) for 0 <= k <= n. G.f.: Sum_{n>=0, k=0..n} T(n,k) * x^k * t^n = t*(1+x-3*x*t) / ((1-t)^2 * (1-2*x*t)^2). Sum_{k=0..n} (-1)^k * binomial(n,k) * T(n,k) = 0 for n >= 0. Sum_{k=0..n} binomial(n,k) * T(n,k) = 2*n * 3^(n-1) for n >= 0. Define the array B(n,p) = (Sum_{k=0..n} binomial(p+k,p) * T(n,k))/(n+p+1) for n >= 0 and p >= 0. Then see the comment of Robert Coquereaux (2014) at A193844. Conjecture: B(n+1,p) = A(n,p). (End) EXAMPLE Triangle starts: 0; 1, 1; 2, 3, 4; 3, 5, 8, 12; 4, 7, 12, 20, 32; ... MAPLE A062111 := proc(n, k) (k+n)*2^(k-n-1) ; end: A152920 := proc(n, k) A062111(n-k, n) ; end: for n from 0 to 15 do for k from 0 to n do printf("%d, ", A152920(n, k)) ; od: od: # R. J. Mathar, Jan 22 2009 MATHEMATICA t[0, k_] := k; t[n_, k_] := t[n, k] = t[n - 1, k] + t[n - 1, k + 1]; Table[t[n - k, k], {n, 0, 10}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Sep 11 2016 *) CROSSREFS Cf. A001787, A193844, A212697. Columns : A001787, A001792, A045623, A045891, A034007, A111297, A159694, A159695, A159696, A159697. [Philippe Deléham, Apr 20 2009] Sequence in context: A342552 A078908 A159797 * A288778 A290139 A317588 Adjacent sequences:  A152917 A152918 A152919 * A152921 A152922 A152923 KEYWORD nonn,tabl,easy AUTHOR Paul Curtz, Dec 15 2008 EXTENSIONS Edited by N. J. A. Sloane, Dec 19 2008 More terms from R. J. Mathar, Jan 22 2009 STATUS approved

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Last modified April 18 18:20 EDT 2021. Contains 343089 sequences. (Running on oeis4.)