A134006 a(n) = 1^n + 3^n + 5^n + 7^n.
4, 16, 84, 496, 3108, 20176, 134004, 903856, 6161988, 42326416, 292299924, 2026332016, 14085959268, 98111307856, 684331371444, 4778093436976, 33385561506948, 233393582580496, 1632228682596564, 11417969833962736
Offset: 0
Keywords
Examples
a(3)=84 because 1^2+3^2+5^2+7^2=84.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
- T. A. Gulliver, Divisibility of sums of powers of odd integers, Int. Math. For. 5 (2010) 3059-3066, eq. 6.
- Index entries for linear recurrences with constant coefficients, signature (16, -86, 176, -105).
Programs
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Magma
[1^n + 3^n + 5^n + 7^n: n in [0..30]]; // Vincenzo Librandi, Jun 20 2011
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Mathematica
Table[1^n+3^n+5^n+7^n,{n,0,30}] -
PARI
{a(n) = 1^n + 3^n + 5^n + 7^n}; /* Michael Somos, Jun 29 2017 */
Formula
a(n) = 15*a(n-1) - 71*a(n-2) + 105*a(n-3) - 48.
G.f.: 1 / (1 - x) + 1 / (1 - 3*x) + 1 / (1 - 5*x) + 1 / (1 - 7*x), E.g.f.: exp(x) + exp(3*x) + exp(5*x) + exp(7*x). - Michael Somos, Jun 29 2017