A258806 a(n) = n^7 + 1.

1, 2, 129, 2188, 16385, 78126, 279937, 823544, 2097153, 4782970, 10000001, 19487172, 35831809, 62748518, 105413505, 170859376, 268435457, 410338674, 612220033, 893871740, 1280000001, 1801088542, 2494357889, 3404825448, 4586471425, 6103515626, 8031810177

Offset: 0

Author

Vincenzo Librandi, Jun 11 2015

Keywords

• nonn
• easy

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Subsequence of A004864.

Sequences of the type n^k+1: A002522 (k=2), A001093 (k=3), A002523 (k=4), A002561 (k=5), A002604 (k=6), this sequence (k=7), A060890 (k=8).

Cf. A300785.

Programs

GAP

List([0..30],n->n^7+1); # Muniru A Asiru, Oct 24 2018

Magma

[n^7+1: n in [0..40]];

Magma

I:=[1,2,129,2188, 16385,78126,279937,823544]; [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]];

Maple

seq(n^7+1,n=0..30); # Muniru A Asiru, Oct 24 2018

Mathematica

Table[n^7 + 1, {n, 0, 40}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 2, 129, 2188, 16385, 78126, 279937, 823544}, 40]

PARI

a(n)=n^7+1 \\ Charles R Greathouse IV, Jun 11 2015

Sage

[n^7+1 for n in (1..40)] # Bruno Berselli, Jun 11 2015

Formula

G.f.: (1 - 6*x + 141*x^2 + 1156*x^3 + 2451*x^4 + 1170*x^5 + 127*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) = (n + 1)*(n^6 - n^5 + n^4 - n^3 + n^2 - n + 1).

a(n) = Sum_{k=0..n} A300785(n,k). - Kolosov Petro, Oct 23 2018

E.g.f.: (1 +x +63*x^2 +301*x^3 +350*x^4 +140*x^5 +*21*x^6 +x^7)*exp(x). - G. C. Greubel, Oct 24 2018