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A061316 a(n) = n*(n+1)*(n^2 + n + 4)/4. 5
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; text; internal format)
OFFSET

0,2

LINKS

Harry J. Smith, Table of n, a(n) for n=0,...,1000

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

FORMULA

a(n) = n*(n+1)*(n^2 + n + 4)/4.

a(n) = 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. - Harvey P. Dale, May 03 2011

MAPLE

a:=n->sum((n+j^3), j=0..n): seq(a(n), n=0..36); # Zerinvary Lajos, Jul 27 2006

with(combinat):a:=n->sum(fibonacci(4, i), i=0..n): seq(a(n), n=0..36); # Zerinvary Lajos, Mar 20 2008

MATHEMATICA

s=0; lst={}; Do[s+=n^3+n*2; AppendTo[lst, s], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, 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] (* Harvey P. Dale, May 03 2011 *)

PROG

(PARI) { for (n=0, 1000, write("b061316.txt", n, " ", n*(n + 1)*(n^2 + n + 4)/4) ) } \\ Harry J. Smith, Jul 21 2009

CROSSREFS

Sequence in context: A328111 A135622 A316853 * A124161 A089580 A034564

Adjacent sequences:  A061313 A061314 A061315 * A061317 A061318 A061319

KEYWORD

nonn

AUTHOR

Henry Bottomley, Apr 24 2001

STATUS

approved

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Last modified October 28 17:59 EDT 2021. Contains 348329 sequences. (Running on oeis4.)