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A160827 a(n) = 3*n^4+12*n^3+30*n^2+36*n+17. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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).

FORMULA

a(n) = Sum_{i=0..2} A000583(n+i) = Sum_{j=n..n+2} j^4.

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

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 *)

PROG

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

(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

CROSSREFS

Cf. A008514.

Sequence in context: A044268 A044649 A253707 * A231671 A231675 A231679

Adjacent sequences:  A160824 A160825 A160826 * A160828 A160829 A160830

KEYWORD

nonn,easy

AUTHOR

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

EXTENSIONS

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

STATUS

approved

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Last modified August 21 02:25 EDT 2017. Contains 290855 sequences.