login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A322141 a(n) is also the sum of the even-indexed terms of the n-th row of the triangle A237591. 3
0, 0, 1, 1, 2, 1, 2, 2, 2, 3, 4, 3, 4, 5, 4, 4, 5, 5, 6, 5, 6, 7, 8, 7, 7, 8, 9, 8, 9, 8, 9, 9, 10, 11, 10, 10, 11, 12, 13, 12, 13, 12, 13, 14, 13, 14, 15, 14, 14, 14, 15, 16, 17, 16, 17, 16, 17, 18, 19, 18, 19, 20, 19, 19, 20, 19, 20, 21, 22, 21, 22, 20, 21 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..73.

Omar E. Pol, Illustration of A237593 as an isosceles triangle (rows: 1..28)

Omar E. Pol, Perspective view of the pyramid (first 16 levels)

FORMULA

a(n) = n - A240542(n).

EXAMPLE

Illustration of initial terms in two ways:

.

n    a(n)

1      0

2      0                     _                                      _

3      1                    |_|                                   _|_|

4      1                   _|_|                                 _|_|

5      2                  |_ _|                               _|_ _|

6      1                 _|_|                               _|_|

7      2                |_ _|                             _|_ _|

8      2               _|_ _|                           _|_ _|

9      2              |_ _|  _                        _|_ _|

10     3             _|_ _| |_|                     _|_ _|_|

11     4            |_ _ _| |_|                   _|_ _ _|_|

12     3           _|_ _|   |_|                 _|_ _|_|

13     4          |_ _ _|  _|_|               _|_ _ _|_|

14     5         _|_ _ _| |_ _|             _|_ _ _|_ _|

15     4        |_ _ _|   |_|             _|_ _ _|_|

16     4        |_ _ _|   |_|            |_ _ _|_|

...

                    Figure 1.                       Figure 2.

.

Figure 1 shows the illustration of initial terms taken from the isosceles triangle of A237593 (see link). For n = 16 there are (3 + 1) = 4 cells in the 16th row of the diagram, so a(16) = 4.

Figure 2 shows the illustration of initial terms taken from an octant of the pyramid described in A244050 and A245092 (see link). For n = 16 there are (3 + 1) = 4 cells in the 16th row of the diagram, so a(16) = 4.

Note that if we fold each level (or row) of that isosceles triangle of A237593 we essentially obtain the structure of the pyramid described in A245092 whose terraces at the n-th level have a total area equal to sigma(n) = A000203(n).

PROG

(PARI) row235791(n) = vector((sqrtint(8*n+1)-1)\2, i, 1+(n-(i*(i+1)/2))\i);

row237591(n) = {my(orow = concat(row235791(n), 0)); vector(#orow -1, i, orow[i] - orow[i+1]); }

a003056(n) = floor((sqrt(1+8*n)-1)/2);

a(n) = my(row=row237591(n)); sum(k=1, a003056(n), if (!(k%2), row[k])); \\ Michel Marcus, Dec 22 2020

CROSSREFS

Cf. A000203, A000217, A067742, A237591, A237593, A240542, A244050, A245092, A259177, A286001, A338204, A338758.

Sequence in context: A060715 A108954 A123920 * A029170 A079526 A291708

Adjacent sequences:  A322138 A322139 A322140 * A322142 A322143 A322144

KEYWORD

nonn

AUTHOR

Omar E. Pol, Dec 21 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 22 16:35 EDT 2021. Contains 345388 sequences. (Running on oeis4.)