A160828 a(n) = 4*n^4 + 24*n^3 + 84*n^2 + 144*n + 98.

98, 354, 978, 2258, 4578, 8418, 14354, 23058, 35298, 51938, 73938, 102354, 138338, 183138, 238098, 304658, 384354, 478818, 589778, 719058, 868578, 1040354, 1236498, 1459218, 1710818, 1993698, 2310354, 2663378, 3055458, 3489378, 3968018, 4494354

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), May 27 2009

Keywords

• nonn
• easy

Comments

Sums of 4 consecutive fourth powers.

Subsequence of A217844. - Michel Marcus, Jun 30 2013

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Programs

Magma

[4*n^4+24*n^3+84*n^2+144*n+98: n in [0..40]]; // Vincenzo Librandi, Aug 27 2011

Maple

A000583 := proc(n) n^4 ; end: A160828 := proc(n) add(A000583(i),i=n..n+3) ; end: seq(A160828(n),n=0..40) ; # R. J. Mathar, May 29 2009

Mathematica

Table[4n^4+24n^3+84n^2+144n+98,{n,0,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{98,354,978,2258,4578},40] (* Harvey P. Dale, Mar 25 2012 *)
CoefficientList[Series[(18*x^4 -72*x^3 +188*x^2 -136*x +98)/(1-x)^5, {x, 0, 50}], x] (* G. C. Greubel, Apr 30 2018 *)

PARI

x='x+O('x^50); Vec((18*x^4 -72*x^3 +188*x^2 -136*x +98)/(1-x)^5) \\ G. C. Greubel, Apr 30 2018

Python

A160828_list, m = [], [96, 0, 80, 80, 98]
for _ in range(10**2):
    A160828_list.append(m[-1])
    for i in range(4):
        m[i+1] += m[i] # Chai Wah Wu, Jan 23 2016

Formula

a(n) = Sum_{i=0..3} A000583(n+i) = Sum_{j=n..n+3} j^4 = A160827(n) + (n+3)^4.

G.f.: (18*x^4 - 72*x^3 + 188*x^2 - 136*x + 98)/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009

a(0)=98, a(1)=354, a(2)=978, a(3)=2258, a(4)=4578, a(n)=5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Harvey P. Dale, Mar 25 2012

E.g.f.: 2*(49 + 128*x + 92*x^2 + 24*x^3 + 2*x^4)*exp(x). - G. C. Greubel, Apr 30 2018

Extensions

Edited and corrected by R. J. Mathar, May 29 2009