A145917 Triangle read by rows: to get n-th row, start with -4n and successively add 5, 7, 9, 11, 13, ... until reaching a square.

0, -4, 1, -8, -3, 4, -12, -7, 0, 9, -16, -11, -4, 5, 16, -20, -15, -8, 1, 12, 25, -24, -19, -12, -3, 8, 21, 36, -28, -23, -16, -7, 4, 17, 32, 49, -32, -27, -20, -11, 0, 13, 28, 45, 64, -36, -31, -24, -15, -4, 9, 24, 41, 60, 81, -40, -35, -28, -19, -8, 5, 20, 37, 56, 77, 100, -44, -39, -32, -23, -12

Offset

0,2

Comments

Row n has n+1 entries.

T(n,k) = n^2-4*k, n, k > = 0 read by antidiagonals. T(n,k) is discriminant the quadratic equation x^2+n*x+k=0. - Boris Putievskiy, Jan 11 2013

Links

Boris Putievskiy, Rows n = 1..140 of triangle, flattened

Boris Putievskiy, Transformations (of) Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

Formula

From Boris Putievskiy, Jan 11 2013: (Start)

a(n) = (A002260(n)-1)^2 - 4*(A004736(n)-1), n >0.

a(n) = (i-1)^2-4(j-1), n>0, where

i = n-t*(t+1)/2,

j = (t*t+3*t+4)/2-n,

t = floor((-1+sqrt(8*n-7))/2). (End)

Crossrefs

Sequence in context: A271478 A112032 A199049 * A201661 A376815 A263498

Adjacent sequences: A145914 A145915 A145916 * A145918 A145919 A145920

Keyword

tabl,sign

Author

Jared Ricks (jaredricks(AT)yahoo.com), Oct 24 2008

Status

approved