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 A156348 Triangle T(n,k) read by rows. Column of Pascal's triangle interleaved with k-1 zeros. 10
 1, 1, 1, 1, 0, 1, 1, 2, 0, 1, 1, 0, 0, 0, 1, 1, 3, 3, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 4, 0, 4, 0, 0, 0, 1, 1, 0, 6, 0, 0, 0, 0, 0, 1, 1, 5, 0, 0, 5, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 6, 10, 10, 0, 6, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS The rows of the Pascal triangle are here found as square root parabolas like in the plots at www.divisorplot.com. Central binomial coefficients are found at the square root boundary. A156348 * A000010 = A156834: (1, 2, 3, 5, 5, 12, 7, 17, 19, 30, 11, ...). - Gary W. Adamson, Feb 16 2009 Row sums give A157019. LINKS Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened el Houcein el Abdalaoui, Mohamed Dahmoune and Djelloul Ziadi, On the transition reduction problem for finite automata, arXiv preprint arXiv:1301.3751 [cs.FL], 2013. - From N. J. A. Sloane, Feb 12 2013 Jeff Ventrella, Divisor Plot EXAMPLE Table begins: 1 1  1 1  0  1 1  2  0  1 1  0  0  0  1 1  3  3  0  0  1 1  0  0  0  0  0  1 1  4  0  4  0  0  0  1 1  0  6  0  0  0  0  0  1 1  5  0  0  5  0  0  0  0  1 1  0  0  0  0  0  0  0  0  0  1 1  6 10 10  0  6  0  0  0  0  0  1 1  0  0  0  0  0  0  0  0  0  0  0  1 1  7  0  0  0  0  7  0  0  0  0  0  0  1 1  0 15  0 15  0  0  0  0  0  0  0  0  0  1 1  8  0 20  0  0  0  8  0  0  0  0  0  0  0  1 1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1 1  9 21  0  0 21  0  0  9  0  0  0  0  0  0  0  0  1 1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1 1 10  0 35 35  0  0  0  0 10  0  0  0  0  0  0  0  0  0  1 MAPLE A156348 := proc(n, k)     if k < 1 or k > n then         return 0 ;     elif n mod k = 0 then         binomial(n/k-2+k, k-1) ;     else         0 ;     end if; end proc: # R. J. Mathar, Mar 03 2013 MATHEMATICA T[n_, k_] := Which[k < 1 || k > n, 0, Mod[n, k] == 0, Binomial[n/k - 2 + k, k - 1], True, 0]; Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 16 2017 *) PROG (Haskell)  Following Mathar's Maple program. a156348 n k = a156348_tabl !! (n-1) !! (k-1) a156348_tabl = map a156348_row [1..] a156348_row n = map (f n) [1..n] where    f n k = if r == 0 then a007318 (n' - 2 + k) (k - 1) else 0            where (n', r) = divMod n k -- Reinhard Zumkeller, Jan 31 2014 CROSSREFS Cf. A007318, A051731,A156834. Sequence in context: A216282 A147861 A167271 * A306437 A343746 A227990 Adjacent sequences:  A156345 A156346 A156347 * A156349 A156350 A156351 KEYWORD nonn,tabl,easy,look AUTHOR Mats Granvik, Feb 08 2009 STATUS approved

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Last modified May 11 06:28 EDT 2021. Contains 343784 sequences. (Running on oeis4.)