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A115514 Triangle read by rows: row n >= 1 lists first n positive members of A004526 (integers repeated) in decreasing order. 4
1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 1, 3, 3, 2, 2, 1, 1, 4, 3, 3, 2, 2, 1, 1, 4, 4, 3, 3, 2, 2, 1, 1, 5, 4, 4, 3, 3, 2, 2, 1, 1, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Sum of terms in row n = A002620(n+1). - Gary W. Adamson, Oct 25 2007

Equals A000012 * A128174 - Gary W. Adamson, Oct 25 2007

T(n,k) = number of 2-element subsets of {1,2,...,n+2} such that the absolute difference of the elements is k+1, where 1 <= k < = n. E.g., T(7,3) = 3, the subsets are {1,5}, {2,6}, and {3,7}. - Christian Barrientos, Jun 27 2022

LINKS

Table of n, a(n) for n=1..105.

FORMULA

T(n, k) = [x^k] p(n), where p(n) are partial Gaussian polynomials (A008967) defined by p(n) = Sum_{k=0..n} Sum_{j=0..n-k} even(k)*x^j, and even(k) = 1 if k is even and otherwise 0. We assume offset 0. - Peter Luschny, Jun 03 2021

T(n, k) = floor((n+2-k)/2). - Christian Barrientos, Jun 27 2022

EXAMPLE

Triangle begins:

  {1}, <- this is row 1

  {1, 1},

  {2, 1, 1},

  {2, 2, 1, 1},

  {3, 2, 2, 1, 1},

  {3, 3, 2, 2, 1, 1},

  {4, 3, 3, 2, 2, 1, 1}

  ...

MAPLE

# Assuming offset 0:

Even := n -> (1 + (-1)^n)/2: # Iverson's even.

p := n -> add(add(Even(k)*x^j, j = 0..n-k), k = 0..n):

for n from 0 to 9 do seq(coeff(p(n), x, k), k=0..n) od; # Peter Luschny, Jun 03 2021

CROSSREFS

Cf. A008967, A000012, A000073, A004526, A128174, A002620.

Sequence in context: A102523 A323023 A083415 * A326038 A122632 A176809

Adjacent sequences:  A115511 A115512 A115513 * A115515 A115516 A115517

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Mar 07 2006

EXTENSIONS

Edited by N. J. A. Sloane, Mar 23 2008 and Dec 15 2017

STATUS

approved

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Last modified September 27 19:35 EDT 2022. Contains 357063 sequences. (Running on oeis4.)