A226492 -id:A226492 - cp's OEIS frontend

A195021 a(n) = n(14n - 11).

0, 3, 34, 93, 180, 295, 438, 609, 808, 1035, 1290, 1573, 1884, 2223, 2590, 2985, 3408, 3859, 4338, 4845, 5380, 5943, 6534, 7153, 7800, 8475, 9178, 9909, 10668, 11455, 12270, 13113, 13984, 14883, 15810, 16765, 17748, 18759, 19798, 20865, 21960, 23083, 24234, 25413

Offset: 0

Omar E. Pol, Sep 07 2011

Sequence found by reading the first two vertices [0, 3] together with the line from 34, in the direction 34, 93, ..., in the Pythagorean spiral whose edges have length A195019 and whose vertices are the numbers A195020, which is related to the primitive Pythagorean triple [3, 4, 5]. For another version see A195030.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A144555, A185019, A193053, A195019, A195020, A195023, A195024, A195025, A195030, A195320, A198017.

Cf. numbers of the form n*(n*k - k + 6)/2, this sequence is the case k=28: see Comments lines of A226492.

[14*n^2 - 11*n: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011

Table[n*(14*n - 11), {n, 0, 50}] (* Paolo Xausa, Jan 15 2025 *)

a(n)=n*(14*n-11) \\ Charles R Greathouse IV, Oct 07 2015

a(n) = 14*n^2 - 11*n.
From Colin Barker, Apr 09 2012: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(3+25*x)/(1-x)^3. (End)
E.g.f.: exp(x)*x*(3 + 14*x). - Elmo R. Oliveira, Dec 30 2024

Edited by Bruno Berselli, Oct 18 2011

A180223 a(n) = (11n^2 - 7n)/2.

Original entry on oeis.org

0, 2, 15, 39, 74, 120, 177, 245, 324, 414, 515, 627, 750, 884, 1029, 1185, 1352, 1530, 1719, 1919, 2130, 2352, 2585, 2829, 3084, 3350, 3627, 3915, 4214, 4524, 4845, 5177, 5520, 5874, 6239, 6615, 7002, 7400, 7809, 8229, 8660

Offset: 0

Graziano Aglietti (mg5055(AT)mclink.it), Aug 16 2010

This sequence is related to A050441 by n*a(n) - Sum_{i=0..n-1} a(i) = 2*A050441(n). - Bruno Berselli, Aug 19 2010
Sum of n-th heptagonal number (A000566) and n-th octagonal number (A000567). - Bruno Berselli, Jun 11 2013
Create a triangle with T(r,1) = r^2 and T(r,c) = r^2 + r*c + c^2. The difference of the sum of the terms in row n and those in row n-1 is a(n). - J. M. Bergot, Jun 17 2013

B. Berselli, Table of n, a(n) for n = 0..10000.
B. Berselli, A description of the recursive method in Comments lines: website Matem@ticamente (in Italian).
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A050441, A000566, A000567, A226492.

Cf. numbers of the form n*(n*k-k+4)/2 listed in A226488 (this sequence is the case k=11). - Bruno Berselli, Jun 10 2013

List([0..30], n-> n*(11*n-7)/2); # G. C. Greubel, Sep 18 2019

[(11*n^2 - 7*n)/2: n in [0..30]]; // Vincenzo Librandi, Apr 18 2011

A180223:=n->(11*n^2 - 7*n)/2; seq(A180223(n), n=0..30); # Wesley Ivan Hurt, Feb 25 2014

Table[(11*n^2 - 7*n)/2, {n, 0, 30}] (* Wesley Ivan Hurt, Feb 25 2014 *)
LinearRecurrence[{3,-3,1},{0,2,15},50] (* Harvey P. Dale, Oct 10 2020 *)

PARI
```
a(n)=1/2*(11*n^2 - 7*n);
```

[n*(11*n-7)/2 for n in (0..30)] # G. C. Greubel, Sep 18 2019

G.f.: x*(2+9*x)/(1-x)^3. - Bruno Berselli, Aug 19 2010 - corrected in Apr 18 2011
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) with n>2. - Bruno Berselli, Aug 19 2010
a(n) = n + A226492(n). - Bruno Berselli, Jun 11 2013
E.g.f.: x*(4 + 11*x)*exp(x)/2. - G. C. Greubel, Aug 24 2015

A017425 a(n) = 11*n + 3.

Original entry on oeis.org

3, 14, 25, 36, 47, 58, 69, 80, 91, 102, 113, 124, 135, 146, 157, 168, 179, 190, 201, 212, 223, 234, 245, 256, 267, 278, 289, 300, 311, 322, 333, 344, 355, 366, 377, 388, 399, 410, 421, 432, 443, 454, 465, 476, 487, 498, 509, 520, 531, 542, 553, 564, 575, 586

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008593, A017401, A017413, A226492.

[11*n+3: n in [0..60]]; // Vincenzo Librandi, Sep 02 2011

11Range[0,50]+3  (* Harvey P. Dale, Apr 21 2011 *)

a(n)=11*n+3 \\ Charles R Greathouse IV, Jul 10 2016

[i+3 for i in range(475) if gcd(i,11) == 11] # Zerinvary Lajos, May 21 2009

From Elmo R. Oliveira, Apr 03 2024: (Start)
G.f.: (3+8*x)/(1-x)^2.
E.g.f.: exp(x)*(3 + 11*x).
a(n) = A226492(n+1) - A226492(n).
a(n) = 2*a(n-1) - a(n-2) for n >= 2. (End)

Terms corrected by Vincenzo Librandi, Sep 02 2011

cp's OEIS Frontend

A195021 a(n) = n*(14*n - 11).

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A180223 a(n) = (11*n^2 - 7*n)/2.

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A017425 a(n) = 11*n + 3.

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Author

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Programs

Magma

Mathematica

PARI

Sage

Formula

Extensions

A195021 a(n) = n(14n - 11).

A180223 a(n) = (11n^2 - 7n)/2.