login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A226449 a(n) = n*(5*n^2-8*n+5)/2. 8
0, 1, 9, 39, 106, 225, 411, 679, 1044, 1521, 2125, 2871, 3774, 4849, 6111, 7575, 9256, 11169, 13329, 15751, 18450, 21441, 24739, 28359, 32316, 36625, 41301, 46359, 51814, 57681, 63975, 70711, 77904, 85569, 93721, 102375, 111546, 121249, 131499, 142311, 153700 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Sequences of the type b(m)+m*b(m-1), where b is a polygonal number:

A006003(n) = A000217(n) + n*A000217(n-1)      (b = triangular numbers);

A069778(n) = A000290(n+1) + (n+1)*A000290(n)  (b = square numbers);

A143690(n) = A000326(n+1) + (n+1)*A000326(n)  (b = pentagonal numbers);

A212133(n) = A000384(n) + n*A000384(n-1)      (b = hexagonal numbers);

a(n)       = A000566(n) + n*A000566(n-1)      (b = heptagonal numbers);

A226450(n) = A000567(n) + n*A000567(n-1)      (b = octagonal numbers);

A226451(n) = A001106(n) + n*A001106(n-1)      (b = nonagonal numbers);

A204674(n) = A001107(n+1) + (n+1)*A001107(n)  (b = decagonal numbers).

LINKS

Bruno Berselli, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

G.f.: x*(1+5*x+9*x^2)/(1-x)^4.

a(n) - a(-n) = A008531(n) for n>0.

MATHEMATICA

Table[n (5 n^2 - 8 n + 5)/2, {n, 0, 40}]

CoefficientList[Series[x (1 + 5 x + 9 x^2)/(1 - x)^4, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 18 2013 *)

LinearRecurrence[{4, -6, 4, -1}, {0, 1, 9, 39}, 50] (* Harvey P. Dale, May 19 2017 *)

PROG

(MAGMA) [n*(5*n^2-8*n+5)/2: n in [0..40]];

(MAGMA) I:=[0, 1, 9, 39]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..45]]; // Vincenzo Librandi, Aug 18 2013

(PARI) a(n)=n*(5*n^2-8*n+5)/2 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. (see the comment) A000566, A006003, A069778, A143690, A204674, A212133, A226450, A226451.

Sequence in context: A192608 A158447 A281381 * A299280 A023163 A054121

Adjacent sequences:  A226446 A226447 A226448 * A226450 A226451 A226452

KEYWORD

nonn,easy

AUTHOR

Bruno Berselli, Jun 07 2013

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 December 14 19:27 EST 2019. Contains 329987 sequences. (Running on oeis4.)