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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
OFFSET
0,1
COMMENTS
Sums of 3 consecutive fourth powers.
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
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 *)
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
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