A104682 a(n) = Sum_{j=0..14} n^j.

1, 15, 32767, 7174453, 357913941, 7629394531, 94036996915, 791260251657, 5026338869833, 25736391511831, 111111111111111, 417724816941565, 1400638324962397, 4265491084507563, 11966776581370171, 31278135027204241, 76861433640456465, 178901440719363487

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Formula

a(n) = 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.

a(n) = (n^2 + n + 1) * (n^4 + n^3 + n^2 + n + 1) * (n^8 - n^7 + n^5 - n^4 + n^3 - n + 1). - Jonathan Vos Post, Apr 23 2005

G.f.: (x^14 +10908*x^13 +3423487*x^12 +162086420*x^11 +2236727781*x^10 +11806635128*x^9 +27116815299*x^8 +28635678216*x^7 +13957353555*x^6 +2999111468*x^5 +253732221*x^4 +6684068*x^3 +32647*x^2 +1)/(1-x)^15. - Colin Barker, Nov 04 2012

Mathematica

With[{f=Total[n^Range[0, 14]]}, Table[f, {n, 0, 20}]] (* Harvey P. Dale, Jun 11 2011 *)

Prog

(Magma) [(&+[n^j: j in [0..14]]): n in [0..20]]; // Vincenzo Librandi, May 01 2011
(PARI) a(n) = sum(j=0, 14, n^j) \\ Charles R Greathouse IV, Oct 07 2015
(Sage) [sum(n^j for j in (0..14)) for n in (0..20)] # G. C. Greubel, Apr 15 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), this sequence (m=14), A105312 (m=15), A269442 (m=16), A269446 (m=18).

Sequence in context: A179106 A157643 A340291 * A185902 A358676 A013756

Adjacent sequences: A104679 A104680 A104681 * A104683 A104684 A104685

Keyword

nonn,easy

Author

Douglas Winston (douglas.winston(AT)srupc.com), Apr 22 2005

Extensions

More terms from Harvey P. Dale, Jun 11 2011

Name changed by G. C. Greubel, Apr 15 2019

Status

approved