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

0,2

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).

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

Example

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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Mathematica

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

Prog

(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

Crossrefs

Cf. A000541, A001015, A022523, A255177.

Sequence in context: A030082 A342349 A017043 * A102061 A080169 A017127

Adjacent sequences: A255178 A255179 A255180 * A255182 A255183 A255184

Keyword

nonn,easy

Author

Luciano Ancora, Mar 18 2015

Extensions

Edited by Bruno Berselli, Mar 19 2015

Status

approved