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A158405
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Table T(n,m) = 1+2*m of odd numbers read along rows, 0<=m<n.
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13
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1, 1, 3, 1, 3, 5, 1, 3, 5, 7, 1, 3, 5, 7, 9, 1, 3, 5, 7, 9, 11, 1, 3, 5, 7, 9, 11, 13, 1, 3, 5, 7, 9, 11, 13, 15, 1, 3, 5, 7, 9, 11, 13, 15, 17, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23
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OFFSET
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1,3
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COMMENTS
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Row sums are n^2 = A000290(n).
Contribution from Johannes W. Meijer, Sep 22 2010: (Start)
The triangle sums, see A180662 for their definitions, link this triangle of odd numbers with seventeen different sequences, see the crossrefs. The knight sums Kn14 - Kn110 have been added.
(End)
A208057 is the eigentriangle of A158405 such that as infinite lower triangular matrices, A158405 * A208057 shifts the latter, deleting the right border of 1's. - Gary W. Adamson, Feb 22 2012
T(n,k) = A099375(n-1,n-k), 1<=k<=n. [Reinhard Zumkeller, Mar 31 2012]
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. A158405 is reluctant sequence of the sequence A005408 the odd numbers. - Boris Putievskiy, Feb 03 2013
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LINKS
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Table of n, a(n) for n=1..78.
Boris Putievskiy, Transformations [of] Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO]
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FORMULA
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a(n)= 2*i-1, where i = n-t(t+1)/2, t = floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Feb 03 2013
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EXAMPLE
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The table contains the first n odd numbers in row n:
1;
1,3;
1,3,5;
1,3,5,7;
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PROG
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(Haskell)
a158405 n k = a158405_row n !! (k-1)
a158405_row n = a158405_tabl !! (n-1)
a158405_tabl = map reverse a099375_tabl
-- Reinhard Zumkeller, Mar 31 2012
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CROSSREFS
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Cf. A129326, A099375, A005408.
Contribution from Johannes W. Meijer, Sep 22 2010: (Start)
Triangle sums (see the comments): A000290 (Row1; Kn11 & Kn4 & Ca1 & Ca4 & Gi1 & Gi4); A000027 (Row2); A005563 (Kn12); A028347 (Kn13); A028560 (Kn14); A028566 (Kn15); A098603 (Kn16); A098847 (Kn17); A098848 (Kn18); A098849 (Kn19); A098850 (Kn110); A000217 (Kn21. Kn22, Kn23, Fi2, Ze2); A000384 (Kn3, Fi1, Ze3); A000212 (Ca2 & Ze4); A000567 (Ca3, Ze1); A011848 (Gi2); A001107 (Gi3).
(End)
Cf. A208057.
Sequence in context: A143732 A130465 A194437 * A113759 A210952 A208523
Adjacent sequences: A158402 A158403 A158404 * A158406 A158407 A158408
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Paul Curtz, Mar 18 2009
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EXTENSIONS
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Edited by R. J. Mathar, Oct 06 2009
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STATUS
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approved
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