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 A124258 Triangle whose rows are sequences of increasing and decreasing squares: 1; 1,4,1; 1,4,9,4,1; ... 6
 1, 1, 4, 1, 1, 4, 9, 4, 1, 1, 4, 9, 16, 9, 4, 1, 1, 4, 9, 16, 25, 16, 9, 4, 1, 1, 4, 9, 16, 25, 36, 25, 16, 9, 4, 1, 1, 4, 9, 16, 25, 36, 49, 36, 25, 16, 9, 4, 1, 1, 4, 9, 16, 25, 36, 49, 64, 49, 36, 25, 16, 9, 4, 1, 1, 4, 9, 16, 25, 36, 49, 64, 81, 64, 49, 36, 25, 16, 9, 4, 1, 1, 4, 9, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The triangle A003983 with individual entries squared and each 2nd row skipped. Analogous to A004737. - Peter Bala, Sep 25 2007 T(n,k) = min(n,k)^2. The order of the list T(n,k) is by sides of squares from T(1,n) to T(n,n), then from T(n,n) to T(n,1). - Boris Putievskiy, Jan 13 2013 LINKS Table of n, a(n) for n=1..85. Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012. FORMULA O.g.f.: (1+qx)^2/((1-x)(1-qx)^2(1-q^2x)) = 1 + x(1 + 4q + q^2) + x^2(1 + 4q + 9q^2 + 4q^3 + q^4) + ... . - Peter Bala, Sep 25 2007 From Boris Putievskiy, Jan 13 2013: (Start) a(n) = (A004737(n))^2. a(n) = (floor(sqrt(n-1)) - |n- floor(sqrt(n-1))^2- floor(sqrt(n-1))-1| +1)^2. (End) EXAMPLE Triangle starts 1; 1, 4, 1; 1, 4, 9, 4, 1: 1, 4, 9, 16, 9, 4, 1: From Boris Putievskiy, Jan 13 2013: (Start) The start of the sequence as table: 1...1...1...1...1...1... 1...4...4...4...4...4... 1...4...9...9...9...9... 1...4...9..16..16..16... 1...4...9..16..25..25... 1...4...9..16..25..36... ... The start of the sequence as triangle array read by rows: 1; 1, 4, 1; 1, 4, 9, 4, 1; 1, 4, 9, 16, 9, 4, 1; 1, 4, 9, 16, 25, 16, 9, 4, 1; 1, 4, 9, 16, 25, 36, 25, 16, 9, 4, 1; ... Row number k contains 2*k-1 numbers 1,4,...,(k-1)^2,k^2,(k-1)^2,...,4,1. (End) MAPLE A003983 := proc(n, k) min(n, k) ; end: A124258 := proc(n, k) A003983(n, k)^2 ; end: for d from 1 to 20 by 2 do for c from 1 to d do printf("%d, ", A124258(d+1-c, c)) ; od: od: # R. J. Mathar, Sep 21 2007 # second Maple program: T:= n-> i^2\$i=1..n, (n-i)^2\$i=1..n-1: seq(T(n), n=1..10); # Alois P. Heinz, Feb 15 2022 MATHEMATICA Flatten[Table[Join[Range[n]^2, Range[n-1, 1, -1]^2], {n, 10}]] (* Harvey P. Dale, Jun 14 2015 *) CROSSREFS Cf. A005900 (row sums), A004737, A133819, A133823, A133824, A133825, A003983. Sequence in context: A246595 A209571 A269845 * A001638 A133826 A209565 Adjacent sequences: A124255 A124256 A124257 * A124259 A124260 A124261 KEYWORD nonn,tabf,easy AUTHOR Jonathan Vos Post, Dec 16 2006 EXTENSIONS More terms from R. J. Mathar, Sep 21 2007 Edited by N. J. A. Sloane, Jun 30 at the suggestion of R. J. Mathar STATUS approved

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Last modified September 7 23:15 EDT 2024. Contains 375749 sequences. (Running on oeis4.)