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 A133819 Triangle whose rows are sequences of increasing squares: 1; 1,4; 1,4,9; ... . 14
 1, 1, 4, 1, 4, 9, 1, 4, 9, 16, 1, 4, 9, 16, 25, 1, 4, 9, 16, 25, 36, 1, 4, 9, 16, 25, 36, 49, 1, 4, 9, 16, 25, 36, 49, 64, 1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Reading the triangle by rows produces the sequence 1,1,4,1,4,9,1,4,9,16,..., analogous to A002260. Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements of the sequence A. A133819 is reluctant sequence of A000290. - Boris Putievskiy, Jan 11 2013 LINKS Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened M. de Frenicle, Methode pour trouver la solutions des problemes par les exclusions, in: Divers ouvrages de mathematiques et de physique par messieurs de l'academie royale des sciences, (1693) pp 1-44, page 11. - Paul Curtz, Aug 18 2008 Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012. FORMULA T(n, k) = k^2, n >= k >= 1. - Wolfdieter Lang, Dec 02 2014 O.g.f.: (1+qx)/((1-x)(1-qx)^3) = 1 + x(1 + 4q) + x^2(1 + 4q + 9q^2) + ... . a(n) = A000290(m+1), where m = n-t(t+1)/2, t = floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Jan 11 2013 EXAMPLE The triangle T(n, k) starts: 1; 1, 4; 1, 4, 9; 1, 4, 9, 16; 1, 4, 9, 16, 25; MATHEMATICA With[{sqs=Range[12]^2}, Flatten[Table[Take[sqs, n], {n, 12}]]] (* Harvey P. Dale, Sep 09 2012 *) PROG (Haskell) a133819 n k = a133819_tabl !! (n-1) !! (k-1) a133819_row n = a133819_tabl !! (n-1) a133819_tabl = map (`take` (tail a000290_list)) [1..] -- Reinhard Zumkeller, Nov 11 2012 CROSSREFS Cf. A215630, A215631, A000290, A002260. Cf. A048152, A060036. Sequence in context: A141225 A344947 A079185 * A344686 A274092 A349039 Adjacent sequences: A133816 A133817 A133818 * A133820 A133821 A133822 KEYWORD easy,nonn,tabl AUTHOR Peter Bala, Sep 25 2007 EXTENSIONS Offset changed by Reinhard Zumkeller, Nov 11 2012 STATUS approved

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Last modified November 27 03:04 EST 2022. Contains 358362 sequences. (Running on oeis4.)