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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.: (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 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 May 25 20:58 EDT 2020. Contains 334597 sequences. (Running on oeis4.)