A255181 Third differences of seventh powers (A001015).

1, 125, 1806, 10206, 35406, 92526, 201726, 388206, 682206, 1119006, 1738926, 2587326, 3714606, 5176206, 7032606, 9349326, 12196926, 15651006, 19792206, 24706206, 30483726, 37220526, 45017406, 53980206, 64219806, 75852126, 88998126, 103783806, 120340206

Offset: 0

Author

Luciano Ancora, Mar 18 2015

Keywords

• nonn
• easy

Examples

			Third differences:   1, 125, 1806, 10206, 35406, ...  (this sequence)
Second differences:  1, 126, 1932, 12138, 47544, ...  (A255177)
First differences:   1, 127, 2059, 14197, 61741, ...  (A022523)
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The seventh powers:  1, 128, 2187, 16384, 78125, ...  (A001015)
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Links

• Lucuano Ancora, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A000541, A001015, A022523, A255177.

Programs

Magma

[1,125] cat [42*(3-10*n+15*n^2-10*n^3+5*n^4): n in [2..30]]; // Vincenzo Librandi, Mar 18 2015

Mathematica

Join[{1, 125}, Table[42 (3 - 10 n + 15 n^2 - 10 n^3 + 5 n^4), {n, 2, 30}]]

Formula

G.f.: (1 + 120*x + 1191*x^2 + 2416*x^3 + 1191*x^4 + 120*x^5 + x^6)/(1 - x)^5.

a(n) = 42*(3 - 10*n + 15*n^2 - 10*n^3 + 5*n^4) for n>1, a(0)=1, a(1)=125.

a(n) = A255177(n)-A255177(n-1). - R. J. Mathar, Jul 16 2015

Extensions

Edited by Bruno Berselli, Mar 19 2015