A140226 Binomial transform of [1, 3, 3, 1, 1, -1, 1, -1, 1, ...].

1, 4, 10, 20, 36, 60, 94, 140, 200, 276, 370, 484, 620, 780, 966, 1180, 1424, 1700, 2010, 2356, 2740, 3164, 3630, 4140, 4696, 5300, 5954, 6660, 7420, 8236, 9110, 10044, 11040, 12100, 13226, 14420

Offset

0,2

Links

Table of n, a(n) for n=0..35.

E. Hetmaniok, M. Pleszczynski, I. Sobstyl, R. Witula, Kaprekar's transformations. Part II-numerical results and intriguing corollaries, Position Papers of the Federated Conference on Computer Science and Information Systems pp. 97-104, ACSIS, Vol. 6; DOI: 10.15439/2015F15.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

A007318 * [1, 3, 3, 1, 1, -1, 1, -1, 1, ...].

From Emeric Deutsch, Jun 03 2008: (Start)

a(n) = n*(11 + n^2)/3 for n >= 1.

G.f.: (1+x^4)/(1-x)^4. (End)

Example

a(5) = 36 = (1, 4, 6, 4, 1) dot (1, 3, 3, 1, 1) = (1 + 12 + 18 + 4 + 1).

Maple

1, seq((1/3)*n*(11+n^2), n=1..35); # Emeric Deutsch, Jun 03 2008

Mathematica

CoefficientList[Series[(1+x^4)/(1-x)^4, {x, 0, 50}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 4, 10, 20, 36}, 50] (* Harvey P. Dale, Aug 17 2021 *)

Prog

(PARI) a(n)=max(n*(11 + n^2)/3, 1) \\ Charles R Greathouse IV, Oct 19 2022

Crossrefs

Sequence in context: A301177 A009847 A362717 * A264924 A008059 A145132

Adjacent sequences: A140223 A140224 A140225 * A140227 A140228 A140229

Keyword

nonn,easy

Author

Gary W. Adamson, May 12 2008

Extensions

More terms from Emeric Deutsch, Jun 03 2008

Status

approved