A160827 a(n) = 3*n^4 + 12*n^3 + 30*n^2 + 36*n + 17.

17, 98, 353, 962, 2177, 4322, 7793, 13058, 20657, 31202, 45377, 63938, 87713, 117602, 154577, 199682, 254033, 318818, 395297, 484802, 588737, 708578, 845873, 1002242, 1179377, 1379042, 1603073, 1853378, 2131937, 2440802, 2782097, 3158018, 3570833

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

Sums of 3 consecutive fourth powers.

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).

Crossrefs

Cf. A008514.

Programs

Magma

[3*n^4+12*n^3+30*n^2+36*n+17: n in [0..40]]; // Vincenzo Librandi, Aug 27 2011

Maple

A000583 := proc(n) n^4 ; end: A160827 := proc(n) add(A000583(i),i=n..n+2) ; end: seq(A160827(n),n=0..40) ; # R. J. Mathar, May 29 2009

Mathematica

Total/@Partition[Range[0,40]^4,3,1] (* or *) LinearRecurrence[{5,-10,10,-5,1},{17,98,353,962,2177},40] (* Harvey P. Dale, Nov 16 2014 *)
CoefficientList[Series[(2*x^4+7*x^3+33*x^2+13*x+17)/(1-x)^5, {x, 0, 50}], x] (* G. C. Greubel, Apr 30 2018 *)

PARI

a(n)=3*n^4+12*n^3+30*n^2+36*n+17 \\ Charles R Greathouse IV, Oct 16 2015

Python

A160827_list, m = [], [72, -36, 30, 15, 17]
for _ in range(10**2):
    A160827_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..2} A000583(n+i) = Sum_{j=n..n+2} j^4.

G.f.: (2*x^4+7*x^3+33*x^2+13*x+17)/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009

E.g.f.: (17 + 81*x + 87*x^2 + 30*x^3 + 3*x^4)*exp(x). - G. C. Greubel, Apr 30 2018

Extensions

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