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A128076 A128064 * A004736. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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*k-2 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 -(m-1)*A002260.

a(n) = m*(t+1) + (m-1)*(t*(t+1)/2-n), where t=floor((-1+sqrt(8*n-7))/2).

For m = 2

a(n) = 2*A003056 -A002260.

a(n) = 2*(t+1)+(t*(t+1)/2-n), where t=floor((-1+sqrt(8*n-7))/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

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Last modified April 19 11:17 EDT 2019. Contains 322264 sequences. (Running on oeis4.)