A258808 a(n) = n^7 - 1.
0, 127, 2186, 16383, 78124, 279935, 823542, 2097151, 4782968, 9999999, 19487170, 35831807, 62748516, 105413503, 170859374, 268435455, 410338672, 612220031, 893871738, 1279999999, 1801088540, 2494357887, 3404825446, 4586471423, 6103515624, 8031810175
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
Programs
-
Magma
[n^7-1: n in [1..40]];
-
Magma
I:=[0,127,2186,16383, 78124,279935,823542,2097151]; [n le 8 select I[n] else 8*Self(n-1) - 28*Self(n-2)+56*Self(n-3)-70*Self(n-4)+56*Self(n-5) - 28*Self(n-6) +8*Self(n-7)-Self(n-8): n in [1..40]];
-
Mathematica
Table[n^7 - 1, {n, 1, 40}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 127, 2186, 16383, 78124, 279935, 823542, 2097151}, 40] -
Sage
[n^7-1 for n in (1..40)] # Bruno Berselli, Jun 11 2015
Formula
G.f.: x^2*(127 + 1170*x + 2451*x^2 + 1156*x^3 + 141*x^4 - 6*x^5 + x^6)/(1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).
a(n) = -A024005(n). [Bruno Berselli, Jun 11 2015]
a(n) = (n-1)*A053716(n). - Michel Marcus, Aug 21 2015