login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A257448 a(n) = 13*(2^n - 1) - 3*n^2 - 9*n. 2
1, 9, 37, 111, 283, 657, 1441, 3051, 6319, 12909, 26149, 52695, 105859, 212265, 425161, 851043, 1702903, 3406725, 6814477, 13630095, 27261451, 54524289, 109050097, 218101851, 436205503, 872412957, 1744828021, 3489658311, 6979319059, 13958640729 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

These numbers belong to a family of sequences obtained as follows:

. A000225:   1*(2^n-1);

. A050488:   3*(2^n-1) - 2*n;

.    a(n):  13*(2^n-1) - 3*n^2 -  9*n;

. A257449:  75*(2^n-1) - 4*n^3 - 18*n^2 -  52*n;

. A257450: 541*(2^n-1) - 5*n^4 - 30*n^3 - 130*n^2 - 375*n,

where the sequence 1, 3, 13, 75, 541, ... is A000670 (after the first term), and A208744 gives the triangle of coefficients:

2;

3, 9;

4, 18, 52;

5, 30, 130, 375;

6, 45, 260, 1125, 3246;

7, 63, 455, 2625, 11361, 32781, etc.

Also, the antidiagonal sums in the array are given by the formula (6*n^2 + 6*k*n + (k-1)*k)*(k+n)!/((k+3)!*(n-1)!) for k = 0, 1, 2, 3, 4, ... (see Example field).

LINKS

Table of n, a(n) for n=1..30.

Index entries for linear recurrences with constant coefficients, signature (5, -9, 7, -2).

FORMULA

G.f.: x*(1+4*x+x^2)/((1-x)^3*(1-2*x)).

a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>4. - Ray Chandler, Jul 25 2015

EXAMPLE

By the second comment, the array begins:

k=0: 1,  8, 27,  64,  125,  216, ...  A000578

k=1: 1,  9, 36, 100,  225,  441, ...  A000537

k=2: 1, 10, 46, 146,  371,  812, ...  A024166

k=3: 1, 11, 57, 203,  574, 1386, ...  A101094

k=4: 1, 12, 69, 272,  846, 2232, ...  A101097

k=5: 1, 13, 82, 354, 1200, 3432, ...  A101102

k=6: 1, 14, 96, 450, 1650, 5082, ...  A254469

...

See also A254469 (Example field).

MATHEMATICA

Table[13 (2^n - 1) - 3 n^2 - 9n, {n, 30}]

CoefficientList[Series[x (1 + 4 x + x^2)/((1 - x)^3*(1 - 2 x)), {x, 0, 30}], x] (* Michael De Vlieger, Nov 14 2016 *)

PROG

(Magma) [13*(2^n-1)-3*n^2-9*n: n in [1..30]]; // Vincenzo Librandi, Apr 24 2015

CROSSREFS

Cf. A000225, A000670, A050488, A208744, A257449, A257450.

Sequence in context: A165394 A213570 A271908 * A288415 A026620 A048878

Adjacent sequences:  A257445 A257446 A257447 * A257449 A257450 A257451

KEYWORD

nonn,easy

AUTHOR

Luciano Ancora, Apr 23 2015

EXTENSIONS

Edited by Bruno Berselli, Apr 28 2015

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 26 20:34 EDT 2022. Contains 357036 sequences. (Running on oeis4.)