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A159920 Sums of the antidiagonals of Sundaram's sieve (A159919). 5
4, 14, 32, 60, 100, 154, 224, 312, 420, 550, 704, 884, 1092, 1330, 1600, 1904, 2244, 2622, 3040, 3500, 4004, 4554, 5152, 5800, 6500, 7254, 8064, 8932, 9860, 10850, 11904, 13024, 14212, 15470, 16800, 18204, 19684, 21242, 22880, 24600, 26404 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

For every n >= 2, a(n) is the sum of numbers in the (n-1)-th antidiagonal of the Sundaram sieve. (It is not clear why the offset was set to 2 rather than 1.) Thus, if T[j, k] is the element in row j and column k of the Sundaram sieve, we have a(n) = Sum_{i = 1..n-1} T[i, n-i] = Sum_{i = 1..n-1} (2*i*(n-i) + i + (n-i)) = (n - 1)*n*(n + 4)/3 for the sum of the numbers in the (n-1)-th antidiagonal. - Petros Hadjicostas, Jun 19 2019

LINKS

Table of n, a(n) for n=2..42.

Andrew Baxter, Sundaram's Sieve.

Julian Havil, Sundaram's Sieve, Plus Magazine, March 2009.

New Zealand Maths, Newletter 18, October 2002.

Wikipedia, Sundaram's Sieve.

Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

FORMULA

a(n) = (n - 1)*n*(n + 4)/3 for n > 1.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

a(n) = 2*A005581(n), n > 1.

a(n) = Sum_{i=1..n-1} i*(i + 3). - Wesley Ivan Hurt, Oct 19 2013

EXAMPLE

For n = 5, (4*5*9)/3 = 60. Indeed, T[1, 4] + T[2, 3] + T[3, 2] + T[4, 1] = 13 + 17 + 17 + 13 = 60 for the sum of the terms in the 4th antidiagonal of the Sundaram sieve.

MAPLE

A159920:=n->n*(n-1)*(n+4)/3; seq(A159920(k), k=2..100); # Wesley Ivan Hurt, Oct 19 2013

MATHEMATICA

a[n_]:=(n-1)*n*(n+4)/3; Table[a[n], {n, 2, 60}] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2010 *)

LinearRecurrence[{4, -6, 4, -1}, {4, 14, 32, 60}, 50]  (* Harvey P. Dale, Apr 23 2011 *)

CROSSREFS

Cf. A005581, A159919.

Sequence in context: A001740 A129395 A023539 * A036486 A023627 A023649

Adjacent sequences:  A159917 A159918 A159919 * A159921 A159922 A159923

KEYWORD

nonn,easy

AUTHOR

Russell Walsmith, Apr 26 2009

STATUS

approved

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Last modified April 3 23:48 EDT 2020. Contains 333207 sequences. (Running on oeis4.)