|
| |
|
|
A061316
|
|
n(n+1)*(n^2+n+4)/4.
|
|
4
| |
|
|
0, 3, 15, 48, 120, 255, 483, 840, 1368, 2115, 3135, 4488, 6240, 8463, 11235, 14640, 18768, 23715, 29583, 36480, 44520, 53823, 64515, 76728, 90600, 106275, 123903, 143640, 165648, 190095, 217155, 247008, 279840, 315843, 355215, 398160, 444888
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,1000
|
|
|
FORMULA
| a(n) =n(n+1)*(n^2+n+4)/4 =A005563(A000217(n)) =3*A006007(n) =A061314(n, 2).
a(0)=0, a(1)=3, a(2)=15, a(3)=48, a(4)=120, a(n)=5a(n-1)-10a(n-2)+ 10a(n-3)- 5a(n-4)+a(n-5)
G.f.: (-3 (x + x^3))/(-1 + x)^5 [From Harvey P. Dale, May 03 2011]
|
|
|
MAPLE
| a:=n->sum((n+j^3), j=0..n): seq(a(n), n=0..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 27 2006
with(combinat):a:=n->sum(fibonacci(4, i), i=0..n): seq(a(n), n=0..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 2008
|
|
|
MATHEMATICA
| s=0; lst={}; Do[s+=n^3+n*2; AppendTo[lst, s], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 04 2009]
Table[n(n+1)(n^2+n+4)/4, {n, 0, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {0, 3, 15, 48, 120}, 40] (* From Harvey P. Dale, May 03 2011 *)
|
|
|
PROG
| (PARI) { for (n=0, 1000, write("b061316.txt", n, " ", n*(n + 1)*(n^2 + n + 4)/4) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 21 2009]
|
|
|
CROSSREFS
| Sequence in context: A088108 A163383 A135622 * A124161 A089580 A034564
Adjacent sequences: A061313 A061314 A061315 * A061317 A061318 A061319
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Apr 24 2001
|
| |
|
|
