



1, 3, 2, 5, 4, 3, 7, 6, 5, 4, 9, 8, 7, 6, 5, 11, 10, 9, 8, 7, 6, 13, 12, 11, 10, 9, 8, 7, 15, 14, 13, 12, 11, 10, 9, 8, 17, 16, 15, 14, 13, 12, 11, 10, 9, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10
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OFFSET

1,2


COMMENTS

Row sums = the pentagonal numbers, A000316, starting (1, 5, 12, 22, 35, 51,...). A004736 = (1; 2, 1; 3, 2, 1;...).
From Boris Putievskiy, Jan 24 2013: (Start)
Table T(n,k)=n+2*k2 n, k > 0, read by antidiagonals.
General case A209304. Let m be natural number. The first column of the table T(n,1) is the sequence of the natural numbers A000027. Every next column is formed from previous shifted by m elements.
For m=0 the result is A002260,
for m=1 the result is A002024,
for m=2 the result is A128076,
for m=3 the result is A131914,
for m=4 the result is A209304. (End)


LINKS

Table of n, a(n) for n=1..55.
Boris Putievskiy, Transformations [Of] Integer Sequences And Pairing Functions, arXiv preprint arXiv:1212.2732, 2012.


FORMULA

A128064 * A004736 as infinite lower triangular matrices.
From Boris Putievskiy, Jan 24 2013: (Start)
For the general case
a(n) = m*A003056 (m1)*A002260.
a(n) = m*(t+1) + (m1)*(t*(t+1)/2n), where t=floor((1+sqrt(8*n7))/2).
For m = 2
a(n) = 2*A003056 A002260.
a(n) = 2*(t+1)+(t*(t+1)/2n), where t=floor((1+sqrt(8*n7))/2). (End)


EXAMPLE

First few rows of the triangle are:
1;
3, 2;
5, 4, 3;
7, 6, 5, 4;
9, 8, 7, 6, 5;
...


CROSSREFS

Cf. A128064, A004736, A000326, A003056, A002260, A002024, A131914, A209304.
Sequence in context: A205850 A204890 A239680 * A076243 A140061 A292776
Adjacent sequences: A128073 A128074 A128075 * A128077 A128078 A128079


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Feb 14 2007


STATUS

approved



