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URL: https://oeis.org/A105312

⇱ A105312 - OEIS

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A105312
a(n) = Sum_{j=0..15} n^j.
7
1, 16, 65535, 21523360, 1431655765, 38146972656, 564221981491, 5538821761600, 40210710958665, 231627523606480, 1111111111111111, 4594972986357216, 16807659899548765, 55451384098598320, 167534872139182395, 469172025408063616, 1229782938247303441
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
FORMULA
a(n) = n^15 + n^14 + n^13 + n^12 + n^11 + n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n^1 + 1.
G.f.: (21845*x^14 + 10412160*x^13 + 689427979*x^12 + 12966588160*x^11 + 93207091581*x^10 + 296077418240*x^9 + 446019954555*x^8 + 326065923072*x^7 + 113735241015*x^6 + 17786608768*x^5 + 1095139065*x^4 + 20476160*x^3 + 65399*x^2 +1 )/(x-1)^16. - Colin Barker, Nov 04 2012
MAPLE
a:= n-> add(n^k, k=0..15):
seq(a(n), n=0..20); # Alois P. Heinz, Nov 04 2012
MATHEMATICA
Prepend[Table[Total[n^Range[0, 15]], {n, 20}], 1] (* Harvey P. Dale, Jan 19 2011 *)
PROG
(Magma) [(&+[n^j: j in [0..15]]): n in [0..20]]; // Vincenzo Librandi, May 01 2011 (modified by G. C. Greubel, Apr 14 2019)
(PARI) vector(20, n, n--; sum(j=0, 15, n^j)) \\ G. C. Greubel, Apr 14 2019
(SageMath) [sum(n^j for j in (0..15)) for n in (0..20)] # G. C. Greubel, Apr 14 2019
CROSSREFS
Cf. similar sequences of the type a(n) = Sum_{j=0..m} n^j are: A000027 (m=1), A002061 (m=2), A053698 (m=3), A053699 (m=4), A053700 (m=5), A053716 (m=6), A053717 (m=7), A102909 (m=8), A103623 (m=9), A060885 (m=10), A105067 (m=11), A060887 (m=12), A104376 (m=13), A104682 (m=14), this sequence (m=15), A269442 (m=16), A269446 (m=18).
Sequence in context: A393091 A185141 A087586 * A013758 A078186 A217026
KEYWORD
nonn,easy
AUTHOR
Douglas Winston (douglas.winston(AT)srupc.com), Apr 30 2005
EXTENSIONS
More terms from Harvey P. Dale, Jan 19 2011
Name changed by G. C. Greubel, Apr 14 2019
STATUS
approved