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!)
A338758 a(n) is the sum of even-indexed terms (of every row) of first n rows of the triangle A237591. 3
0, 0, 1, 2, 4, 5, 7, 9, 11, 14, 18, 21, 25, 30, 34, 38, 43, 48, 54, 59, 65, 72, 80, 87, 94, 102, 111, 119, 128, 136, 145, 154, 164, 175, 185, 195, 206, 218, 231, 243, 256, 268, 281, 295, 308, 322, 337, 351, 365, 379, 394, 410, 427, 443, 460, 476, 493, 511, 530, 548, 567, 587, 606, 625 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..64.

FORMULA

a(n) = A000217(n) - A338204(n).

EXAMPLE

Illustration of a(16) = 38 in two ways:

.

Level

1

2                            _                                      _

3                           |_|                                   _|_|

4                          _|_|                                 _|_|

5                         |_ _|                               _|_ _|

6                        _|_|                               _|_|

7                       |_ _|                             _|_ _|

8                      _|_ _|                           _|_ _|

9                     |_ _|  _                        _|_ _|

10                   _|_ _| |_|                     _|_ _|_|

11                  |_ _ _| |_|                   _|_ _ _|_|

12                 _|_ _|   |_|                 _|_ _|_|

13                |_ _ _|  _|_|               _|_ _ _|_|

14               _|_ _ _| |_ _|             _|_ _ _|_ _|

15              |_ _ _|   |_|             _|_ _ _|_|

16              |_ _ _|   |_|            |_ _ _|_|

...

                    Figure 1.                       Figure 2.

.

For n = 16, figure 1 shows the illustration of a(16) taken from the isosceles triangle of A237593. There are 38 cells in the first 16 levels of the diagram, so a(16) = 38.

Figure 2 shows the illustration of a(16) taken from an octant of the pyramid described in A244050 and A245092. There are 38 cells in the first 16 levels of the diagram, so a(16) = 38.

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);

a322141(n) = my(row=row237591(n)); sum(k=1, a003056(n), if (!(k%2), row[k]));

a(n) = sum(k=1, n, a322141(k)); \\ Michel Marcus, Dec 22 2020

CROSSREFS

Partial sums of A322141.

Cf. A000217, A067742, A237591, A237593, A240542, A259177, A286001, A338204.

Sequence in context: A186388 A058577 A071917 * A051060 A116650 A140205

Adjacent sequences:  A338755 A338756 A338757 * A338759 A338760 A338761

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 April 18 15:54 EDT 2021. Contains 343089 sequences. (Running on oeis4.)